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Dynamical Systems
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Work-in-progress lecture notes for a two-semester course on Dynamical Systems. Topics covered include: topological dynamics, chaos theory, ergodic theory, hyperbolic and complex dynamics.
50. The Omega Stability Theorem
Published
2 years ago
Dynamical Systems
49. No Cycles
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2 years ago
Dynamical Systems
Problem Sheet T
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2 years ago
Dynamical Systems
48. The Spectral Decomposition Theorem
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2 years ago
Dynamical Systems
47: Homoclinic Tangles
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2 years ago
Dynamical Systems
46. The Inclination Lemma
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2 years ago
Dynamical Systems
45. Axiom A and the Anosov Closing Lemma
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2 years ago
Dynamical Systems
44. The Shadowing Theorem
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2 years ago
Dynamical Systems
Problem Sheet S
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2 years ago
Dynamical Systems
43. Isolated Hyperbolic Sets
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2 years ago
Dynamical Systems
42. Hyperbolicity Implies Weak Structural Stability
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2 years ago
Dynamical Systems
41. Structural Stability
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2 years ago
Dynamical Systems
40. The Stable Manifold Theorem for Hyperbolic Sets
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2 years ago
Dynamical Systems
Problem Sheet R
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2 years ago
Dynamical Systems
39. Lifting Dynamical Systems
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2 years ago
Dynamical Systems
38. Persistence of Hyperbolic Sets
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2 years ago
Dynamical Systems
Problem Sheet Q
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2 years ago
Dynamical Systems
37. Hyperbolic Sets
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2 years ago
Dynamical Systems
36. Introduction to Riemannian Geometry
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2 years ago
Dynamical Systems
35. Introduction to Differential Geometry
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2 years ago
Dynamical Systems
34. The Stable Manifold Theorem
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2 years ago
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Problem Sheet P
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2 years ago
Dynamical Systems
33. Stable and Unstable Manifolds
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2 years ago
Dynamical Systems
32. The Hartman-Grobman Theorem
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2 years ago
Dynamical Systems
31. Persistence of Hyperbolic Fixed Points
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2 years ago
Dynamical Systems
Problem Sheet O
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2 years ago
Dynamical Systems
30. Hyperbolic Fixed Points
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2 years ago
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29. Hyperbolic Linear Dynamical Systems
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2 years ago
Dynamical Systems
Problem Sheet N
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2 years ago
Dynamical Systems
28. The Variational Principle
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2 years ago
Dynamical Systems
27. Measure-Theoretic Entropy
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2 years ago
Dynamical Systems
Problem Sheet M
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2 years ago
Dynamical Systems
26. Partitions and the Rokhlin Metric
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2 years ago
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25. Unique Ergodicity
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2 years ago
Dynamical Systems
Problem Sheet L
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2 years ago
Dynamical Systems
24. Finding Invariant Measures
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2 years ago
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23. Measures on Metric Spaces
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2 years ago
Dynamical Systems
Problem Sheet K
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2 years ago
Dynamical Systems
22. Spectral Properties of Dynamical Systems
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2 years ago
Dynamical Systems
21. Mixing from a Measure-Theoretic Viewpoint
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2 years ago
Dynamical Systems
Problem Sheet J
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2 years ago
Dynamical Systems
20. The Birkhoff Ergodic Theorem
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2 years ago
Dynamical Systems
19. Ergodicity
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2 years ago
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Problem Sheet I
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2 years ago
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18. The Denjoy Theorem
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2 years ago
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17. The Poincaré Classification Theorem
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2 years ago
Dynamical Systems
Problem Sheet H
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2 years ago
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16. Rational Rotation Numbers
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2 years ago
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15. Rotation Numbers
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2 years ago
Dynamical Systems
Problem Sheet G
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2 years ago
Dynamical Systems
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