Unit 6 - Week - 4

Chaotic Dynamical Systems - - Unit 6 - Week - 4 https://onlinecourses.nptel.ac.in/noc18_ma02/un...

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Unit 6 - Week - 4

Course outline Assignment 4 The due date for submitting this assignment has passed. Due on 2018-02-21, 23:59 IST. How to access the portal Submitted assignment

Assignment 0 Pick the correct options from each question. There is no negative marking. 1) The formulation of Horse-shoe attractor was made by; 4 points Week-1

Week - 2 John Littlewood.

Week - 3 Stephen Smale. Week - 4

Nonlinear Systems Mary Cartwright.

Horseshoe Attractor Norman Levinson.

Dynamics of the No, the answer is incorrect. Horseshoe Score: 0 Attractor. Accepted Answers: Quiz : Assignment Stephen Smale. 4 2) For a Dynamical system, which of the following is/are true for an attractor; 4 points Solutions of Assignment 4.

Week - 5 Attractor is a closed subset of the system.

Week - 6 Attractor is an open subset of the system.

Week - 7 Attractor is a completely invariant subset of the system. Week - 8

Any bounded subset is an attractor. Week - 9 No, the answer is incorrect. Week - 10 Score: 0 Accepted Answers: Week - 11 Attractor is a closed subset of the system. Attractor is a completely invariant subset of the system. Week - 12 3) In the Smale Horse shoe (∧, f ); 4 points

The set of periodic points is dense.

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1 of 3 Thursday 17 May 2018 02:15 PM Chaotic Dynamical Systems - - Unit 6 - Week - 4 https://onlinecourses.nptel.ac.in/noc18_ma02/un...

There are finitely many periodic points.

No, the answer is incorrect. Score: 0 Accepted Answers: The set of periodic points is dense. There is a periodic point of every order.

4) In the symbolic system (Σ, σ) i.e; ({0, 1}ℤ, σ) discussed in the lecture; 4 points

There is no fixed point.

There are infinitely many fixed points.

There are exactly two fixed points.

There are odd number of fixed points.

No, the answer is incorrect. Score: 0 Accepted Answers: There are exactly two fixed points.

5) Which of the following is/are true for the Smale Horse shoe (∧, f ); 4 points

The system contains no minimal subset.

The system itself is a minimal system.

The map f is a homeomorphism.

This system contains a dense orbit.

No, the answer is incorrect. Score: 0 Accepted Answers: The map f is a homeomorphism.

This system contains a dense orbit.

6) Which of the following is/are true in (Σ, σ); 4 points

All sequences which has even number of zeros between any two ones are periodic points under

⎯⎯ ⎯⎯ s , where . W (0) = ⋃m∈ℤ{{xn}n∈ℤ : xn = 0 or 1 and xn = 0, n > m} 0 = … 00 … 0.0 … 00 …

(Σ, σ) is a countable space.

For every natural number n, there are only finitely many periodic points of period n.

No, the answer is incorrect. Score: 0 Accepted Answers: ⎯⎯ ⎯⎯ s , where . W (0) = ⋃m∈ℤ{{xn}n∈ℤ : xn = 0 or 1 and xn = 0, n > m} 0 = … 00 … 0.0 … 00 … For every natural number n, there are only finitely many periodic points of period n.

2 of 3 Thursday 17 May 2018 02:15 PM Chaotic Dynamical Systems - - Unit 6 - Week - 4 https://onlinecourses.nptel.ac.in/noc18_ma02/un...

7) The Smale Horse Shoe (∧, f ) is; 4 points

Compact.

Not compact.

Connected space.

Disconnected Space.

No, the answer is incorrect. Score: 0 Accepted Answers: Compact. Disconnected Space.

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