Subject Code: MA7L017	Subject Name:  Ergodic Theory and Dynamical Systems	L-T-P: 3-1-0	Credit:4
Pre-requisite(s): Topology (MA5L008), Measure Theory (MA5L014)
Examples and Basic concepts:  Dynamical system, orbits,  Circle rotations, Shifts and sub-shifts, Hyperbolic toral automorphisms, The Horseshoe, The solenoid, Flows and differential equations, Chaos and Lyapunov exponents; Topological dynamics: Limit sets, Recurrence, Mixing, Transitivity, Entropy; Symbolic Dynamics:  Subshifts, Sofic shifts, codes, Perron Frobenius Theorem, Data storage; Ergodic Theory:  Ergodicity and mixing, Ergodic theorems (Von Neumann Ergodic Theorem, Birkhoff Ergodic Theorem), Invariant measures for continuous maps,;  Unique ergodicity and Weyl’s theorem, Discrete spectrum, Weak mixing, Internet search;  Hyperbolic dynamics: Stable and unstable manifolds, Anosov diffeomorphisms, Axiom A and structural stability; Ergodicity of Anosov diffeomorphisms: Holder continuity of the stable and unstable distributions, Absolute continuity of stable and unstable foliations;
Text/Reference Books: Brin M.  and Stuck G.  Introduction to Dynamical Systems, Cambridge University Press Pollicott  M. and Yuri M. Dynamical systems and Ergodic Theory, Cambridge University Press