Download this article
 Download this article For screen
For printing
Recent Issues

Volume 28
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Geodesic coordinates for the pressure metric at the Fuchsian locus

Xian Dai

Geometry & Topology 27 (2023) 1391–1478
Bibliography
1 L V Ahlfors, Some remarks on Teichmüller’s space of Riemann surfaces, Ann. of Math. 74 (1961) 171 MR204641
2 D Baraglia, G2 geometry and integrable systems, preprint (2010) arXiv:1002.1767
3 R Bowen, Markov partitions for Axiom A diffeomorphisms, Amer. J. Math. 92 (1970) 725 MR277003
4 R Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973) 429 MR339281
5 R Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, 470, Springer (2008) MR2423393
6 R Bowen, D Ruelle, The ergodic theory of Axiom A flows, Invent. Math. 29 (1975) 181 MR380889
7 M Bridgeman, R Canary, F Labourie, Simple length rigidity for Hitchin representations, Adv. Math. 360 (2020) MR4035950
8 M Bridgeman, R Canary, F Labourie, A Sambarino, The pressure metric for Anosov representations, Geom. Funct. Anal. 25 (2015) 1089 MR3385630
9 M Bridgeman, R Canary, F Labourie, A Sambarino, Simple root flows for Hitchin representations, Geom. Dedicata 192 (2018) 57 MR3749423
10 S Choi, W M Goldman, Convex real projective structures on closed surfaces are closed, Proc. Amer. Math. Soc. 118 (1993) 657 MR1145415
11 T Chu, The Weil–Petersson metric in the moduli space, Chinese J. Math. 4 (1976) 29 MR590105
12 D Gilbarg, N S Trudinger, Elliptic partial differential equations of second order, 224, Springer (1983) MR737190
13 W M Goldman, Convex real projective structures on compact surfaces, J. Differential Geom. 31 (1990) 791 MR1053346
14 N J Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987) 59 MR887284
15 N J Hitchin, Lie groups and Teichmüller space, Topology 31 (1992) 449 MR1174252
16 A Katok, Entropy and closed geodesics, Ergodic Theory Dynam. Systems 2 (1982) 339 MR721728
17 A Katok, B Hasselblatt, Introduction to the modern theory of dynamical systems, 54, Cambridge Univ. Press (1995) MR1326374
18 M Kotani, T Sunada, The pressure and higher correlations for an Anosov diffeomorphism, Ergodic Theory Dynam. Systems 21 (2001) 807 MR1836433
19 F Labourie, Anosov flows, surface groups and curves in projective space, Invent. Math. 165 (2006) 51 MR2221137
20 F Labourie, R Wentworth, Variations along the Fuchsian locus, Ann. Sci. Éc. Norm. Supér. 51 (2018) 487 MR3798306
21 Q Li, Harmonic maps for Hitchin representations, Geom. Funct. Anal. 29 (2019) 539 MR3945839
22 A N Livšic, Certain properties of the homology of Y –systems, Mat. Zametki 10 (1971) 555 MR293669
23 A N Livšic, Cohomology of dynamical systems, Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972) 1296 MR0334287
24 J Loftin, Survey on affine spheres, from: "Handbook of geometric analysis, II" (editors L Ji, P Li, R Schoen, L Simon), Adv. Lect. Math. 13, International (2010) 161 MR2743442
25 H Masur, M Wolf, The Weil–Petersson isometry group, Geom. Dedicata 93 (2002) 177 MR1934697
26 C T McMullen, Thermodynamics, dimension and the Weil–Petersson metric, Invent. Math. 173 (2008) 365 MR2415311
27 W Parry, M Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, 187–188, Soc. Math. France (1990) 268 MR1085356
28 M Pollicott, On the rate of mixing of Axiom A flows, Invent. Math. 81 (1985) 413 MR807065
29 M Pollicott, Derivatives of topological entropy for Anosov and geodesic flows, J. Differential Geom. 39 (1994) 457 MR1274128
30 M. Pollicott, Multiple mixing for hyperbolic flows, preprint (2012)
31 R Potrie, A Sambarino, Eigenvalues and entropy of a Hitchin representation, Invent. Math. 209 (2017) 885 MR3681396
32 M Ratner, Markov partitions for Anosov flows on n–dimensional manifolds, Israel J. Math. 15 (1973) 92 MR339282
33 A Sambarino, Quantitative properties of convex representations, Comment. Math. Helv. 89 (2014) 443 MR3229035
34 A Sambarino, The orbital counting problem for hyperconvex representations, Ann. Inst. Fourier (Grenoble) 65 (2015) 1755 MR3449196
35 C T Simpson, Constructing variations of Hodge structure using Yang–Mills theory and applications to uniformization, J. Amer. Math. Soc. 1 (1988) 867 MR944577
36 A J Tromba, Teichmüller theory in Riemannian geometry, Birkhäuser (1992) 220 MR1164870
37 M Wolf, The Teichmüller theory of harmonic maps, J. Differential Geom. 29 (1989) 449 MR982185
38 S Wolpert, Noncompleteness of the Weil–Petersson metric for Teichmüller space, Pacific J. Math. 61 (1975) 573 MR422692
39 S A Wolpert, Geodesic length functions and the Nielsen problem, J. Differential Geom. 25 (1987) 275 MR880186