Dynamical systems and ergodic theory University of Bordeaux
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I. HOMEOMORPHISMS OF THE CIRCLE: ROTATION NUMBERS, 1. Poincaré Theorem 2. Denjoy Theorem II. SOME EXAMPLES:1. Gradient flow (in particular of a Morse function),2. Geodesic flow on hyperbolic surfaces,3. Linear Anosov diffeomorphisms.III. SYMBOLIC DYNAMIC.1.Sub shifts of finite type,2.Coding of rotations, expansions on the circle and Smale'shorseshoe,3.Markov's partitions for the linear automorphisms of the torus.IV. DYNAMIC COMPLEXITY.1. Topological entropy,2. Explicit computation for the above examples,3. Entropyand action in homology.V. ELEMENTS OF ERGODIC THEORY.1.Invariant measures (Krylov-Bogolubov Theorem, Birkhoff Theorem).2.Recurrence Theorems (Poincaré and others).3.Ergodicity of linear Anosov maps and of geodesic flow forthe Liouville measure (Hopf Argument).VI. HYPERBOLIC DYNAMICS1. Stable Manifold Theorem, hyperbolic sets,2. Examples: Plykinattractor, Smale solenoid,3. Shadowing lemma and specification,4. Structural stability,5. Conley Theoryand global hyperbolic Theory.VII. DYNAMICS ON HOMOGENOUS SPACES(HOWE-MOORE THEOREM, ETC?) ORPESIN'S THEORY.1.Homeomorphisms of the circle: rotation numbers, Poincaré Theorem.Denjoy Theorem.
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Thisis a course of the M2ALGANT(Algebra,eometry and Number Theory). Formore information about this Master visit thewebpage: https://uf-mi.u-bordeaux.fr/algant/[https://uf-mi.u-bordeaux.fr/algant/]Duration: 12 weeks (spring semester)Language of instruction: EnglishMode of delivery: Face-to-face teaching
Site for Inquiry
Please inquire about the courses at the address below.
Contact person: Nicolas Gourmelonnicolas.gourmelon@u-bordeaux.fr