Dynamical Systems

70 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.

50. The Omega Stability Theorem

Published 6 months ago

Dynamical Systems

49. No Cycles

Published 6 months ago

Dynamical Systems

Problem Sheet T

Published 6 months ago

Dynamical Systems

48. The Spectral Decomposition Theorem

Published 6 months ago

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47: Homoclinic Tangles

Published 6 months ago

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46. The Inclination Lemma

Published 7 months ago

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45. Axiom A and the Anosov Closing Lemma

Published 7 months ago

Dynamical Systems

44. The Shadowing Theorem

Published 7 months ago

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Problem Sheet S

Published 7 months ago

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43. Isolated Hyperbolic Sets

Published 7 months ago

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42. Hyperbolicity Implies Weak Structural Stability

Published 7 months ago

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41. Structural Stability

Published 7 months ago

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40. The Stable Manifold Theorem for Hyperbolic Sets

Published 8 months ago

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Problem Sheet R

Published 8 months ago

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39. Lifting Dynamical Systems

Published 8 months ago

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38. Persistence of Hyperbolic Sets

Published 8 months ago

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Problem Sheet Q

Published 8 months ago

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37. Hyperbolic Sets

Published 8 months ago

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36. Introduction to Riemannian Geometry

Published 8 months ago

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35. Introduction to Differential Geometry

Published 9 months ago

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34. The Stable Manifold Theorem

Published 9 months ago

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Problem Sheet P

Published 9 months ago

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33. Stable and Unstable Manifolds

Published 9 months ago

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32. The Hartman-Grobman Theorem

Published 9 months ago

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31. Persistence of Hyperbolic Fixed Points

Published 9 months ago

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Problem Sheet O

Published 9 months ago

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30. Hyperbolic Fixed Points

Published 9 months ago

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29. Hyperbolic Linear Dynamical Systems

Published 9 months ago

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Problem Sheet N

Published a year ago

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28. The Variational Principle

Published a year ago

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27. Measure-Theoretic Entropy

Published a year ago

Dynamical Systems

Problem Sheet M

Published a year ago

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26. Partitions and the Rokhlin Metric

Published a year ago

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25. Unique Ergodicity

Published a year ago

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Problem Sheet L

Published a year ago

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24. Finding Invariant Measures

Published a year ago

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23. Measures on Metric Spaces

Published a year ago

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Problem Sheet K

Published a year ago

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22. Spectral Properties of Dynamical Systems

Published a year ago

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21. Mixing from a Measure-Theoretic Viewpoint

Published a year ago

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Problem Sheet J

Published a year ago

Dynamical Systems

20. The Birkhoff Ergodic Theorem

Published a year ago

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19. Ergodicity

Published a year ago

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Problem Sheet I

Published a year ago

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18. The Denjoy Theorem

Published a year ago

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17. The Poincaré Classification Theorem

Published a year ago

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Problem Sheet H

Published a year ago

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16. Rational Rotation Numbers

Published a year ago

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15. Rotation Numbers

Published a year ago

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Problem Sheet G

Published a year ago

Dynamical Systems

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