Horocycle dynamics (Part 2) - TIB AV-Portal

Horocycle dynamics (Part 2)

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Institut Fourier

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Title

Horocycle dynamics (Part 2)

Title of Series

Summer School 2018 - Teichmüller dynamics, mapping class groups and applications

Number of Parts

50

Author

License

CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.

Identifiers

10.5446/63386 (DOI)

Publisher

Institut Fourier

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Abstract

A major challenge in dynamics on moduli spaces is to understand the behavior of the horocycle flow. We will motivate this problem and discuss what is known and what is not known about it, focusing on the genus 2 case. Specific topics to be covered include: * SL_2(R) orbit closures and invariant measures in genus 2. * Quantitative nondivergence. * The structure of minimal sets. * Rel and real-rel, and their interaction with the horocycle flow * Horizontal data diagrams and other invariants for horocycle invariant measures. * Classification of measures and orbit-closures in the eigenform loci. * Recent and not-so-recent examples of unexpected measures and orbit-closures.

Series

Summer School 2018 - Teichmüller dynamics, mapping class groups and applications34 / 50

1

1:01:32

Counting closed geodesics on translation surfaces

2

1:00:38

Limit sets of Teichmuller geodesic rays in the Thurston boundary of Teichmuller space

3

1:03:17

Mirzakhani's work on Earthquakes (Part 1)

4

1:01:22

Mirzakhani's work on Earthquakes (Part 3)

5

1:11:31

Mirzakhani's work on Earthquakes (Part 2)

6

1:03:54

Nearly Fuchsian surface subgroups of finite covolume Kleinian groups

7

1:09:24

Counting simple closed geodesics and volumes of moduli spaces (Part 1)

8

1:12:00

Counting simple closed geodesics and volumes of moduli spaces (Part 2)

9

1:11:55

Counting simple closed geodesics and volumes of moduli spaces (Part 3)

10

1:01:04

Monodromy of algebraic families of curves (Part 1)

11

1:31:15

Monodromy of algebraic families of curves (Part 2)

12

1:11:15

Monodromy of algebraic families of curves (Part 3)

13

1:30:18

Horocycle dynamics (Part 1)

14

1:00:38

Horocycle dynamics (Part 2)

15

57:35

Systoles in translation surfaces

16

1:02:45

Teichmüller spaces and pseudo-Anosov homeomorphism (Part 3)

17

1:08:38

Teichmüller spaces and pseudo-Anosov homeomorphism (Part 2)

18

1:22:33

Teichmüller spaces and pseudo-Anosov homeomorphism (Part 1)

19

1:05:50

Square tiled surfaces (Part 1)

20

1:03:49

Square tiled surfaces (Part 2)

21

1:18:11

Square tiled surfaces (Part 3)

22

1:05:26

Billiards, quadrilaterals and moduli spaces

23

53:00

Diffusion rate for windtree models

24

1:02:36

Are affine invariant submanifolds affine

25

53:09

Periodic paths on the pentagon

26

1:01:29

Cohomological equation and Ruelle resonnences (Part 3)

27

1:04:55

Cohomological equation and Ruelle resonnences (Part 1)

28

1:08:16

Cohomological equation and Ruelle resonnences (Part 2)

29

54:22

Deligne-Mostow lattices and cone metrics on the sphere

30

59:19

MCG and infinite MCG (Part 1)

31

1:04:44

MCG and infinite MCG (Part 2)

32

1:28:28

MCG and infinite MCG (Part 3)

33

1:29:11

Horocycle dynamics (Part 1)

34

1:02:15

Horocycle dynamics (Part 2)

35

1:00:16

Minimal dilatations on nonorientable surfaces

36

59:45

Triangle tiling billiards : a hopscotch guided by an interval exchange transformation with flips

37

45:26

Algorithms for multicurves with Dynnikov coordinates

38

58:05

Marked points in genus two and beyond

39

1:41:56

Rauzy gasket, Arnoux-Yoccoz interval exchange map, Novikov's problem (Part 2)

40

1:09:14

Rauzy gasket, Arnoux-Yoccoz interval exchange map, Novikov's problem (Part 1)

41

59:44

Quaternionic monodromies of the Kontsevich–Zorich cocycle

42

57:17

Quantum representations of surface groups

43

1:00:39

K3 surfaces and Dynamics (Part 1)

44

1:01:41

K3 surfaces and Dynamics (Part 2)

45

1:01:17

K3 surfaces and Dynamics (Part 3)

46

59:35

Diophantine interval exchange maps

47

1:07:05

Rauzy gasket, Arnoux-Yoccoz interval exchange map, Novikov's problem (Part 1)

48

1:18:07

Rauzy gasket, Arnoux-Yoccoz interval exchange map, Novikov's problem (Part 2)

49

1:03:20

An introduction to veering triangulations

50

56:07

Effective convergence of ergodic averages and cusp excursions of geodesics

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