Dynamical Systems

54 posts

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.

Problem Sheet Q

Published 4 days ago

Dynamical Systems

37. Hyperbolic Sets

Published 4 days ago

Dynamical Systems

36. Introduction to Riemannian Geometry

Published 7 days ago

Dynamical Systems

35. Introduction to Differential Geometry

Published 11 days ago

Dynamical Systems

34. The Stable Manifold Theorem

Published 15 days ago

Dynamical Systems

Problem Sheet P

Published 20 days ago

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33. Stable and Unstable Manifolds

Published 20 days ago

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32. The Hartman-Grobman Theorem

Published 23 days ago

Dynamical Systems

31. Persistence of Hyperbolic Fixed Points

Published a month ago

Dynamical Systems

Problem Sheet O

Published a month ago

Dynamical Systems

30. Hyperbolic Fixed Points

Published a month ago

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29. Hyperbolic Linear Dynamical Systems

Published a month ago

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Problem Sheet N

Published 3 months ago

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28. The Variational Principle

Published 3 months ago

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27. Measure-Theoretic Entropy

Published 3 months ago

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Problem Sheet M

Published 3 months ago

Dynamical Systems

26. Partitions and the Rokhlin Metric

Published 3 months ago

Dynamical Systems

25. Unique Ergodicity

Published 4 months ago

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Problem Sheet L

Published 4 months ago

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24. Finding Invariant Measures

Published 4 months ago

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23. Measures on Metric Spaces

Published 4 months ago

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Problem Sheet K

Published 4 months ago

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22. Spectral Properties of Dynamical Systems

Published 4 months ago

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21. Mixing from a Measure-Theoretic Viewpoint

Published 4 months ago

Dynamical Systems

Problem Sheet J

Published 4 months ago

Dynamical Systems

20. The Birkhoff Ergodic Theorem

Published 4 months ago

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19. Ergodicity

Published 4 months ago

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Problem Sheet I

Published 4 months ago

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18. The Denjoy Theorem

Published 4 months ago

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17. The Poincaré Classification Theorem

Published 4 months ago

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Problem Sheet H

Published 5 months ago

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16. Rational Rotation Numbers

Published 5 months ago

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15. Rotation Numbers

Published 5 months ago

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Problem Sheet G

Published 5 months ago

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14. The Sharkovsky Theorem

Published 5 months ago

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13. Turbulent Dynamical Systems

Published 5 months ago

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Problem Sheet F

Published 5 months ago

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12. Chaos Versus Positive Entropy

Published 5 months ago

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11. Piecewise Monotone Dynamical Systems

Published 5 months ago

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Problem Sheet E

Published 5 months ago

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10. Topological Entropy via Open Covers

Published 5 months ago

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9. Expansive Dynamical Systems

Published 5 months ago

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Problem Sheet D

Published 5 months ago

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8. Hyperbolic Toral Automorphisms

Published 5 months ago

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7. Topological Entropy

Published 6 months ago

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Problem Sheet C

Published 6 months ago

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6. Furstenberg's Theorem

Published 6 months ago

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5. Mixing and Weakly Mixing Dynamical Systems

Published 6 months ago

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Problem Sheet B

Published 6 months ago

Dynamical Systems

4. What Is Chaos?

Published 6 months ago

Dynamical Systems

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