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Week - 1 |
The definition and examples of dynamical system |
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Week - 2 |
Iteration of functions: Types of orbits; Fixed points, Periodic points |
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Week - 3 |
Contraction mapping and the contraction mapping theorem |
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Week - 4 |
Period-3 theorem |
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Week - 5 |
Sharkovsky theorem |
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Week - 6 |
Attracting and repulsive periodic points |
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Week - 7 |
The tent map, The doubling map |
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Week - 8 |
The logistic map, Families of functions; Bifurcations; |
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Week - 9 |
Cantor set |
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Week - 10 |
Symbolic Dynamics: The squence space, the shift map |
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Week - 11 |
Chaos: Sensitive dependence on Initial Conditions |
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Week - 12 |
Transitivity, Topological conjugacy |
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Week - 13 |
Two dimensional chaos: the Henon map |
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Week - 14 |
The Horseshoe map |
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