MULES and SADDLES Part I
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Saddle-Nodes and Period-Doublings of Smale Horseshoes: a Case Study Near Resonant Homoclinic Bellows
Saddle-nodes and period-doublings of Smale horseshoes: a case study near resonant homoclinic bellows Ale Jan Homburg KdV Institute for Mathematics, University of Amsterdam e-mail: [email protected] Alice C. Jukes Department of Mathematics, Imperial College London email: [email protected] Jurgen¨ Knobloch Department of Mathematics, TU Ilmenau e-mail: [email protected] Jeroen S.W. Lamb Department of Mathematics, Imperial College London email: [email protected] December 17, 2007 Abstract In unfoldings of resonant homoclinic bellows interesting bifurcation phe- nomena occur: two suspensed Smale horseshoes can collide and disappear in saddle-node bifurcations (all periodic orbits disappear through saddle-node bifurcations, there are no other bifurcations of periodic orbits), or a suspended horseshoe can go through saddle-node and period-doubling bifurcations of the periodic orbits in it to create an additional \doubled horseshoe". 1 Introduction In these notes we discuss specific homoclinic bifurcations involving multiple ho- moclinic orbits to a hyperbolic equilibrium with a resonance condition among the eigenvalues of the linearized vector field about the equilibrium; the resonant homo- clinic bellows. A homoclinic bellows consists of two homoclinic orbits γ1(t); γ2(t) to a hyperbolic equilibrium with real leading eigenvalues, that are tangent to each other as t ! ∞. If the homoclinic orbits are symmetry related through the action of a Z2 symmetry, the homoclinic bellows is a bifurcation of codimension one (we review the bifurcation theory in x 2); the additional resonance condition makes it a bifurcation of codimension two. 1 The resonant homoclinic bellows is an organizing center for an interesting bifur- cation phenomenon involving suspended Smale horseshoes (this is our motivation for studying the bifurcation). -
A Comprehensive Investigation of Lead Sheathing from the Emanuel
A COMPREHENSIVE INVESTIGATION OF LEAD SHEATHING FROM THE EMANUEL POINT SHIPWRECKS IN PENSACOLA BAY, FLORIDA by Andrew Wallace Marr B.A., Colorado State University, 2006 A thesis submitted to the Department of Anthropology College of Arts and Sciences The University of West Florida In partial fulfillment of the requirements for the degree of Master of Arts 2012 The thesis of Andrew Wallace Marr is approved: ____________________________________________ _________________ Gregory D. Cook, M.A., Committee Member Date ____________________________________________ _________________ Amy Mitchell-Cook, Ph.D., Committee Member Date ____________________________________________ _________________ John E. Worth, Ph.D., Committee Member Date ____________________________________________ _________________ John R. Bratten, Ph.D., Committee Chair Date Accepted for the Department/Division: ____________________________________________ _________________ John R. Bratten, Ph.D., Chair Date Accepted for the University: ____________________________________________ _________________ Richard S. Podemski, Ph.D., Dean, Graduate Studies Date ACKNOWLEDGMENTS This study would never have been possible without the contributions and support of a number of different organizations and individuals. Many facets of my research involved scientific analysis, and I would like to thank Dr. Elizabeth Benchley and the UWF Archaeology Institute, as well as the Pensacola Archaeological Society for their financial support. Without their grants and funding much of this thesis would have gone unwritten. I am very appreciative to my committee for their efforts throughout the course of this study, from helping me to plan the excavations and experimentation to tirelessly editing draft after draft of each of my chapters. I would also like to thank a number of friends and fellow students for their contributions to my research. These include Dr. Felipe Castro, Dr. -
Horse Racing Tack for the Hivewire (HW3D) Horse by Ken Gilliland Horse Racing, the Sport of Kings
Horse Racing Tack for the HiveWire (HW3D) Horse by Ken Gilliland Horse Racing, the Sport of Kings Horse racing is a sport that has a long history, dating as far back as ancient Babylon, Syria, and Egypt. Events in the first Greek Olympics included chariot and mounted horse racing and in ancient Rome, both of these forms of horse racing were major industries. As Thoroughbred racing developed as a sport, it became popular with aristocrats and royalty and as a result achieved the title "Sport of Kings." Today's horse racing is enjoyed throughout the world and uses several breeds of horses including Thoroughbreds and Quarter Horses in the major race track circuit, and Arabians, Paints, Mustangs and Appaloosas on the County Fair circuit. There are four types of horse racing; Flat Track racing, Jump/Steeplechase racing, Endurance racing and Harness racing. “Racehorse Tack” is designed for the most common and popular type of horse racing, Flat Track. Tracks are typically oval in shape and are level. There are exceptions to this; in Great Britain and Ireland there are considerable variations in shape and levelness, and at Santa Anita (in California), there is the famous hillside turf course. Race track surfaces can vary as well with turf being the most common type in Europe and dirt more common in North America and Asia. Newer synthetic surfaces, such as Polytrack or Tapeta, are also seen at some tracks. Individual flat races are run over distances ranging from 440 yards (400 m) up to two and a half miles, with distances between five and twelve furlongs being most common. -
Approved Tack and Equipment for British Dressage Competitions
Approved tack and equipment for British Dressage competitions Eff ective from 17 June 2019 To be used with the corresponding rules in the Members’ Handbook This revised pictorial guide has been devised to be used alongside the British Dressage Members’ Handbook for clarification on permitted tack and equipment. British Dressage endeavours to mirror FEI Rules for permitted tack and equipment. Tack reviews are ongoing but, any additional permitted tack and equipment updates will only be issued twice yearly to coincide with the beginning of the summer and winter seasons (1 December and 18 June). At all BD Championships, there will be an appointed BD Steward(s) in attendance in all warm up arenas responsible for tack and equipment checking every competitor each time they compete. This will be a physical (not just visual) tack check, including nosebands. It’s the organisers’ responsibility to appoint stewards for this function and they must be BD or FEI qualified to the appropriate level, for further guidelines on the official tack check, please see rule 106 in the 2019 Members Handbook. For the complete guidelines on permitted tack and riding the test and penalties, please see section Section 1 of the Members’ Handbook. If the equipment that you are looking at are similar to those pictured, it’s permitted for use in BD competitions. If you have a query on any tack or equipment that you’re unsure about, please email a picture of the item to the Sports Operations Officer for clarification. NB: Please note that bridles without a throatlash will be permitted for use for national competitions, for international competitions please check FEI rules. -
Reproduction of the Early Medieval Knight's Saddle
Reproduction of the Early Medieval Knight’s Saddle by Sir Armand de Sevigny [The following is a re-writing of an article done some ten years ago by Sir Armand for the Caid Leathercrafters Guild’s newsletter Tanned Hydes. Although the errors in the printed portions of that article have been removed, Sir Armand apologizes for the elemental nature of his drawings included therein.] The saddle of the medieval knight was essential to his effectiveness as a heavy cavalryman. By the end of the Eleventh Century the saddle had evolved into the basic form it was to maintain for the next four hundred years. The front piece, the pommel, was high and broad, as was the back of the seat, the cantle. Typically the cantle was curved forward to cradle the knight’s hips. A reproduction of a typical early medieval saddle [1050-1350 AD] can be made by anyone with rudimentary leather and woodworking skills and a degree of patience and imagination. The place to start is with the saddle’s foundation, the saddle “tree”. The tree is basically two shaped wooden “planks” that straddle the horse’s rib cage on either side of the backbone. These planks are secured by the wooden “pommel” and “cantle” fore and aft respectively. Because construction of a well- fitting saddle tree is beyond the artistic capacities of most of us, and because the proper shape and fitting of the tree is absolutely essential to the comfort of the horse, I would recommend against producing your own tree unless you are an expert with horses, saddles, and carpentry to begin with. -
Sand Canyon & Rock Creek Trails
Sand Canyon & Rock Creek Trails Canyons of the Ancients National Monument © Kim Gerhardt CANYONS OF THE ANCIENTS NATIONAL MONUMENT Ernest Vallo, Sr. Canyons of the CANYONS Eagle Clan, Pueblo of Acoma: Ancients National OF THE Monument ANCIENTS MAPS & INFORMATION When we come to and the Anasazi a place like Sand Heritage Center Anasazi Heritage Canyon, we pray Center to the ancestral 27501 Highway 184, Hovenweep people. As Indian Dolores, CO 81323 National Monument Canyons people we believe Tel: (970) 882-5600 of the 491 the spirits are Hours: Ancients still here. National Monument 9–5 Summer Mar.- Oct. We ask them Road G for our strength 10–4 Winter Nov.- Feb. and continued https://www.blm.gov/ 160 Mesa Verde survival, and programs/national- 491 National Park thank them conservation-lands/ colorado/canyons-of-the- for sharing their home place. In the Acoma ancients language I say, “Good morning. I’ve brought A public land administered my friends. If we approached in the wrong way, by the Bureau of Land please excuse our ignorance.” Management. 2 Please Stay on Designated Trails Welcome to the Sand Canyon & Rock Creek Trails 3 anyons of the Ancients National Monument was created to protect cultural and Cnatural resources on a landscape scale. It is part of the Bureau of Land Management’s National Landscape Conservation System and includes almost 171,000 acres of public land. The Sand Canyon and Rock Creek Trails are open for hiking, mountain biking, or horseback riding on designated routes only. Most of the Monument is backcountry. Visitors to Canyons of the Ancients are encouraged to start at the Anasazi Heritage Center near Dolores, Mountain Biking Tips David Sanders Colorado, where they can get current information from local rider Dani Gregory: Park Ranger, Canyons of the Ancients: about the Monument and experience the museum’s • Hikers and bikers are supposed to stop for • All it takes is for exhibits, films, and hands-on discovery area. -
Product Catalogue 1
Leading Brand in Harness & Accessories Product Catalogue 1 www.idealequestrian.com Ideal Equestrian Quality and reassurance Since 1994 Ideal Equestrian has been developing and producing a wide range of driving harness and accessories. The standard of our harness is our no.1 priority and together with successful national and international drivers, we are constantly improving in the design and technology of our products. Our harness ranges from a luxury traditional leather presentation 2 harness with full collar, to a marathon or high-tech synthetic EuroTech harness. Ideal has it all! This catalogue is just a selection of our products. Visit our website and view our full range, and discover what Ideal Equestrian has to offer you. www.idealequestrian.com LEADING BRAND IN HARNESS & ACCESSORIES Index HARNESS Luxe 4 Marathon 6 LeatherTech Combi 8 EuroTech Classic 12 3 EuroTech Combi 14 WebTech Combi 16 Ideal Friesian 18 Ideal Heavy horse 18 Harness Parts 19 Driving Accessories 20 Luxe • Traditional Classic Harness • High Quality Leather • Elegant appearance Sizes available: Full / Cob / Pony / Shetland / Mini Shetland 4 Leather LeatherLeather Leather Black Black/ London Australian Nut Luxe Options – Single: - Breast collar with continuous traces This traditionally made quality harness is perfect for all disciplines of carriage driving, durable enough (adjustment at carriage end) for tough conditions yet attractive for presentation. Nylon webbing is stitched between the leather where extra strength is needed. The saddle pad has foam filled cushions, holes are oval to prevent - Traces with Rollerbolt or Crew hole tearing and all buckles have stainless steel tongues. Nose band is fully adjustable and headpiece is - Leather Reins tapered in the middle to create more freedom around the ears. -
Tory Leather LLC Equestrian Equipment Catalog Proudly Made in the USA TORY and YOU
Tory Leather LLC Equestrian Equipment Catalog Proudly Made in the USA TORY AND YOU As we continue our growth and changes with the merchandise that we manufacture, we must also make changes in order to serve you more proficiently. Following are our Terms and Policies that we ask you to read. • TERMS: Our terms are 2% 10 - Net 30 to approved dealers with accounts in good standing. This means that you can take a 2% discount from the subtotal if paid within 10 days. If you do not pay in that 10 day time, the complete balance is due in 30 days. Do not include the shipping when figuring the 2% discount. • FIRST TIME ORDERS will be shipped C.O.D., Certified Check or Credit Card unless other arrangements are made with the credit manager. • We accept MasterCard, Visa, Discover, and AMEX (AMEX pending approval). • A $10.00 SERVICE CHARGE will be added to all orders under $50.00. • There will be a $25.00 Service Charge on ALL RETURNED CHECKS. • We reserve the right to refuse shipments to accounts with a PAST DUE BALANCE of 30 days or more. • All past due accounts are subject to finance charges. • An account TURNED OVER FOR COLLECTION will be liable for all collection fees and court costs that are involved in settling the account. • Please INSPECT ALL ORDERS ON RECEIVING THEM - ANY SHORTAGES OR DAMAGES MUST BE REPORTED WITHIN 48 HOURS. • No RETURNS will be accepted unless you phone and request a return authorization. Tory will not accept any returned items that are special or custom orders unless defective. -
Saddleology (PDF)
This manual is intended for 4-H use and created for Maine 4-H members, leaders, extension agents and staff. COVER CREATED BY CATHY THOMAS PHOTOS OF SADDLES COURSTESY OF: www.horsesaddleshop.com & www.western-saddle-guide.com & www.libbys-tack.com & www.statelinetack.com & www.wikipedia.com & Cathy Thomas & Terry Swazey (permission given to alter photo for teaching purposes) REFERENCE LIST: Western Saddle Guide Dictionary of Equine Terms Verlane Desgrange Created by Cathy Thomas © Cathy Thomas 2008 TABLE OF CONTENTS Introduction.................................................................................4 Saddle Parts - Western..................................................................5-7 Saddle Parts - English...................................................................8-9 Fitting a saddle........................................................................10-15 Fitting the rider...........................................................................15 Other considerations.....................................................................16 Saddle Types & Functions - Western...............................................17-20 Saddle Types & Functions - English.................................................21-23 Latigo Straps...............................................................................24 Latigo Knots................................................................................25 Cinch Buckle...............................................................................26 Buying the right size -
4-H Driving Manual
4-H Driving Manual A Pacific Northwest Extension Publication Oregon State University • Washington State University • University of Idaho PNW 229 Introduction Use this 4-H Driving Manual as you learn Driving is a valuable training option for light how to train your animal, fit the harness properly, horses, draft horses, ponies, donkeys, mules, and drive your animal safely. The manual or miniature horses. For example, when a 4-H outlines one of several accepted ways of training. member grows too large to ride a pony, he or See “For More Information” (page 27) for she can learn to drive it. A full-size young horse other publications that can help you continue to can be driven before it’s physically ready for expand your knowledge. riding, which shortens training time and gives 4-H members can use the 4-H Driving Manual it experience. A mature riding horse’s value to train any equine to drive. For simplicity’s increases if it can also pull a cart. sake, the manual uses the word “horse” to stand For driving, you need a vehicle and harness. for all equines. Vehicles and harnesses are available in several Words that appear in the text in SMALL CAPS are price ranges through tack stores or catalogs. The found in the Glossary. driver, horse, vehicle, and harness together are referred to as the TURNOUT. The 4-H Driving Manual was developed and written by the Pacific Northwest (PNW) 4-H Driving Publication Committee. The team was led by Erika Thiel, 4-H program coordinator, University of Idaho. -
Goat Tips (Updated July 2020)
Goat Tips (Updated July 2020) It is normal for some goats that are hiking loose to stray 10-20 yards back to eat while you travel, they will run to catch up only to stop and nibble a tasty plant and let you get ahead again. They will rarely let you get out of sight though, this eat and run behavior will decrease as the goat tires after a couple of miles and they fill their belly’s. Most goats file in behind in front or alongside you plodding steadily along on the trail at your pace. If you have two or more goats, you will notice that they seem to compete for positions on the trail after they get it worked out remember the hiking order. If you have to tie the goats together in a string tie them in the proper order attaching the carabineer to the back of the SADDLE, NOT the pannier. It will make the difference between an orderly hike and a tangled mess. When a goat stops in front of you to eat and blocks the trail, keep walking and go around his backside the best you can and he will then turn and start walking again just as you pass him, if unable to pass then act like you are and make the same noise like walking in place, or gently pull on his tail with a “let’s go”. Remember if you stop, they all stop. While walking some goats will push you to the side and off the trail just step back and around the back side of the goat to the other side and then he may start pushing you the other way just keep stepping to the other side they just want to be next to you this should stop in a little while. -
Our Favorite Ropes for Halters, Leads and Reins
Our Favorite ropes for halters, leads and reins. Rope halters, leads and reins are favored by many natural horse trainers. The interaction between the product design and type of rope used creates unique products. Many famous horse trainers have perfected their designs/rope choices to create products tailored to their training methods. This document is our attempt to share the insights/opinions we have developed while selling rope, creating rope tack, and working with trainers over the past twelve years. We hope sharing our insights will help take some of the mystery out of choosing the perfect rope to meet your needs. Sincerely, Columbia Basin Knot Company, LLC rope sales and home of the Knotty Girlz - creating quality rope products in the USA. Diameter Rope Construction Rope diameters used for tying halters typically vary between 3/16 inch to 5/16 inch in diameter. Diameters of 3/16 inch are often used underneath a bridle or for training. One of the more popular Double Braid diameters used by many natural horse trainers is 1/4 inch. While A double braid rope refers to a braided rope cover over a braided 5/16 inch and 3/8 inch can be bulking on small horses, foals, rope core. Basically, it is a rope over another rope. These ropes weanlings, and yearlings, they can work well with larger horses. are often flexible and easy to handle. Most double braid ropes are Commonly requested diameters for lead ropes range from 1/2 inch spliceable. Double braid rope is often called yacht braid and can be to 5/8 inch.