Geometry & Topology Volume 28, issue 5 (2024)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

The asymmetry of Thurston's earthquake flow

Francisco Arana-Herrera and Alex Wright

Geometry & Topology 28 (2024) 2125–2144

DOI: 10.2140/gt.2024.28.2125

Bibliography

1	F Arana-Herrera, Equidistribution of families of expanding horospheres on moduli spaces of hyperbolic surfaces, Geom. Dedicata 210 (2021) 65 MR4200910
2	F Arana-Herrera, Counting hyperbolic multigeodesics with respect to the lengths of individual components and asymptotics of Weil–Petersson volumes, Geom. Topol. 26 (2022) 1291
3	A Avila, S Gouëzel, Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow, Ann. of Math. 178 (2013) 385 MR3071503
4	A Avila, M J Resende, Exponential mixing for the Teichmüller flow in the space of quadratic differentials, Comment. Math. Helv. 87 (2012) 589 MR2980521
5	A Avila, S Gouëzel, J C Yoccoz, Exponential mixing for the Teichmüller flow, Publ. Math. Inst. Hautes Études Sci. 104 (2006) 143 MR2264836
6	L Bakker, T Fisher, Open sets of diffeomorphisms with trivial centralizer in the C¹ topology, Nonlinearity 27 (2014) 2869 MR3291134
7	P Berk, K Frączek, T de la Rue, On typicality of translation flows which are disjoint with their inverse, J. Inst. Math. Jussieu 19 (2020) 1677 MR4138955
8	C Bonatti, I Monteverde, A Navas, C Rivas, Rigidity for C¹ actions on the interval arising from hyperbolicity, I : Solvable groups, Math. Z. 286 (2017) 919 MR3671566
9	W Bonomo, P Varandas, A criterion for the triviality of the centralizer for vector fields and applications, J. Differential Equations 267 (2019) 1748 MR3945616
10	L Burslem, A Wilkinson, Global rigidity of solvable group actions on S¹, Geom. Topol. 8 (2004) 877 MR2087072
11	A Calderon, J Farre, Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow, Geom. Topol. 28 (2024) 1995
12	V Erlandsson, J Souto, Counting curves on orbifolds, Trans. Lond. Math. Soc. 9 (2022) 56 MR4535658
13	B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
14	K Frączek, M Lemańczyk, On the self-similarity problem for ergodic flows, Proc. Lond. Math. Soc. 99 (2009) 658 MR2551467
15	K Frączek, J Kułaga-Przymus, M Lemańczyk, Non-reversibility and self-joinings of higher orders for ergodic flows, J. Anal. Math. 122 (2014) 163 MR3183527
16	S W Fu, Cusp excursions for the earthquake flow on the once-punctured torus, Conform. Geom. Dyn. 23 (2019) 251 MR4033067
17	É Ghys, Actions localement libres du groupe affine, Invent. Math. 82 (1985) 479 MR0811548
18	É Ghys, A Verjovsky, Locally free holomorphic actions of the complex affine group, from: "Geometric study of foliations" (editors T Mizutani, K Masuda, S Matsumoto, T Inaba, T Tsuboi, Y Mitsumatsu), World Sci. (1994) 201 MR1363727
19	N Guelman, I Liousse, C¹–actions of Baumslag–Solitar groups on S¹, Algebr. Geom. Topol. 11 (2011) 1701 MR2821437
20	N Guelman, I Liousse, Actions of Baumslag–Solitar groups on surfaces, Discrete Contin. Dyn. Syst. 33 (2013) 1945 MR3002737
21	J Hubbard, H Masur, Quadratic differentials and foliations, Acta Math. 142 (1979) 221 MR0523212
22	N V Ivanov, Automorphism of complexes of curves and of Teichmüller spaces, Int. Math. Res. Not. 1997 (1997) 651 MR1460387
23	S P Kerckhoff, The Nielsen realization problem, Ann. of Math. 117 (1983) 235 MR0690845
24	M Lipnowski, A Wright, Towards optimal spectral gaps in large genus, Ann. Probab. 52 (2024) 545
25	M Liu, Length statistics of random multicurves on closed hyperbolic surfaces, Groups Geom. Dyn. 16 (2022) 437 MR4502612
26	S Lu, W Su, Counting mapping class group orbits under shearing coordinates, Geom. Dedicata 216 (2022) 16 MR4380058
27	H Masur, The Teichmüller flow is Hamiltonian, Proc. Amer. Math. Soc. 123 (1995) 3739 MR1283559
28	A E McCarthy, Rigidity of trivial actions of abelian-by-cyclic groups, Proc. Amer. Math. Soc. 138 (2010) 1395 MR2578531
29	C T McMullen, Complex earthquakes and Teichmüller theory, J. Amer. Math. Soc. 11 (1998) 283 MR1478844
30	Y Minsky, B Weiss, Nondivergence of horocyclic flows on moduli space, J. Reine Angew. Math. 552 (2002) 131 MR1940435
31	M Mirzakhani, Random hyperbolic surfaces and measured laminations, from: "In the tradition of Ahlfors–Bers, IV" (editors D Canary, J Gilman, J Heinonen, H Masur), Contemp. Math. 432, Amer. Math. Soc. (2007) 179 MR2342816
32	M Mirzakhani, Simple geodesics and Weil–Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent. Math. 167 (2007) 179 MR2264808
33	M Mirzakhani, Ergodic theory of the earthquake flow, Int. Math. Res. Not. 2008 (2008) MR2416997
34	M Mirzakhani, Counting mapping class group orbits on hyperbolic surfaces, preprint (2016) arXiv:1601.03342
35	A Navas, Groups of circle diffeomorphisms, Univ. of Chicago Press (2011) MR2809110
36	A Navas, Group actions on 1–manifolds : a list of very concrete open questions, from: "Proceedings of the International Congress of Mathematicians, III" (editors B Sirakov, P N d Souza, M Viana), World Sci. (2018) 2035 MR3966841
37	D Obata, Symmetries of vector fields: the diffeomorphism centralizer, Discrete Contin. Dyn. Syst. 41 (2021) 4943 MR4284644
38	R C Penner, J L Harer, Combinatorics of train tracks, 125, Princeton Univ. Press (1992) MR1144770
39	M Ratner, The rate of mixing for geodesic and horocycle flows, Ergodic Theory Dynam. Systems 7 (1987) 267 MR0896798
40	J Smillie, B Weiss, Minimal sets for flows on moduli space, Israel J. Math. 142 (2004) 249 MR2085718
41	Y Sözen, F Bonahon, The Weil–Petersson and Thurston symplectic forms, Duke Math. J. 108 (2001) 581 MR1838662
42	W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
43	W P Thurston, Minimal stretch maps between hyperbolic surfaces, preprint (1998) arXiv:math/9801039 MR4554454
44	A Wilkinson, Conservative partially hyperbolic dynamics, from: "Proceedings of the International Congress of Mathematicians, III" (editors R Bhatia, A Pal, G Rangarajan, V Srinivas, M Vanninathan, P Gastesi), Hindustan (2010) 1816 MR2827868
45	A Wilkinson, J Xue, Rigidity of some abelian-by-cyclic solvable group actions on 𝕋^N, Comm. Math. Phys. 376 (2020) 1223 MR4103967
46	A Wright, A tour through Mirzakhani’s work on moduli spaces of Riemann surfaces, Bull. Amer. Math. Soc. 57 (2020) 359 MR4108090
47	A Wright, Mirzakhani’s work on earthquake flow, from: "Teichmüller theory and dynamics" (editors P Dehornoy, E Lanneau), Panor. Synth. 58, Soc. Math. France (2022) 101 MR4563317