Dynamical Systems

42 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 N

Published 25 days ago

Dynamical Systems

28. The Variational Principle

Published a month ago

Dynamical Systems

27. Measure-Theoretic Entropy

Published a month ago

Dynamical Systems

Problem Sheet M

Published a month ago

Dynamical Systems

26. Partitions and the Rokhlin Metric

Published a month ago

Dynamical Systems

25. Unique Ergodicity

Published a month ago

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Problem Sheet L

Published a month ago

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24. Finding Invariant Measures

Published a month ago

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23. Measures on Metric Spaces

Published a month ago

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Problem Sheet K

Published 2 months ago

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22. Spectral Properties of Dynamical Systems

Published 2 months ago

Dynamical Systems

21. Mixing from a Measure-Theoretic Viewpoint

Published 2 months ago

Dynamical Systems

Problem Sheet J

Published 2 months ago

Dynamical Systems

20. The Birkhoff Ergodic Theorem

Published 2 months ago

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19. Ergodicity

Published 2 months ago

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Problem Sheet I

Published 2 months ago

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18. The Denjoy Theorem

Published 2 months ago

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17. The Poincaré Classification Theorem

Published 2 months ago

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Problem Sheet H

Published 2 months ago

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16. Rational Rotation Numbers

Published 2 months ago

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15. Rotation Numbers

Published 2 months ago

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Problem Sheet G

Published 2 months ago

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14. The Sharkovsky Theorem

Published 2 months ago

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13. Turbulent Dynamical Systems

Published 3 months ago

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Problem Sheet F

Published 3 months ago

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12. Chaos Versus Positive Entropy

Published 3 months ago

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11. Piecewise Monotone Dynamical Systems

Published 3 months ago

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Problem Sheet E

Published 3 months ago

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10. Topological Entropy via Open Covers

Published 3 months ago

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9. Expansive Dynamical Systems

Published 3 months ago

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Problem Sheet D

Published 3 months ago

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8. Hyperbolic Toral Automorphisms

Published 3 months ago

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7. Topological Entropy

Published 3 months ago

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Problem Sheet C

Published 3 months ago

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6. Furstenberg's Theorem

Published 3 months ago

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5. Mixing and Weakly Mixing Dynamical Systems

Published 3 months ago

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Problem Sheet B

Published 4 months ago

Dynamical Systems

4. What Is Chaos?

Published 4 months ago

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3. The Non-Wandering Set and Its Friends

Published 4 months ago

Dynamical Systems

2. Transitivity and Minimality

Published 4 months ago

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Problem Sheet A

Published 4 months ago

Dynamical Systems

1. The Definition of a Dynamical System

Published 4 months ago

Dynamical Systems

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