Geometry & Topology Volume 27, issue 8 (2023)

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Anosov representations with Lipschitz limit set

Maria Beatrice Pozzetti, Andrés Sambarino and Anna Wienhard

Geometry & Topology 27 (2023) 3303–3360

DOI: 10.2140/gt.2023.27.3303

Bibliography

1	T Barbot, Three-dimensional Anosov flag manifolds, Geom. Topol. 14 (2010) 153 MR2578303
2	T Barbot, Deformations of Fuchsian AdS representations are quasi-Fuchsian, J. Differential Geom. 101 (2015) 1 MR3356068
3	T Barbot, Q Mérigot, Anosov AdS representations are quasi-Fuchsian, Groups Geom. Dyn. 6 (2012) 441 MR2961282
4	Y Benoist, Propriétés asymptotiques des groupes linéaires, Geom. Funct. Anal. 7 (1997) 1 MR1437472
5	Y Benoist, Convexes divisibles, I, from: "Algebraic groups and arithmetic" (editors S G Dani, G Prasad), Tata Inst. Fund. Res. (2004) 339 MR2094116
6	J Bochi, R Potrie, A Sambarino, Anosov representations and dominated splittings, J. Eur. Math. Soc. 21 (2019) 3343 MR4012341
7	R Bowen, Hausdorff dimension of quasicircles, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 11 MR556580
8	S B Bradlow, O García-Prada, P B Gothen, Deformations of maximal representations in Sp(4, ℝ), Q. J. Math. 63 (2012) 795 MR2999985
9	M Bridgeman, R Canary, F Labourie, A Sambarino, The pressure metric for Anosov representations, Geom. Funct. Anal. 25 (2015) 1089 MR3385630
10	M Burger, A Iozzi, F Labourie, A Wienhard, Maximal representations of surface groups : symplectic Anosov structures, Pure Appl. Math. Q. 1 (2005) 543 MR2201327
11	M Burger, A Iozzi, A Wienhard, Tight homomorphisms and Hermitian symmetric spaces, Geom. Funct. Anal. 19 (2009) 678 MR2563767
12	M Burger, A Iozzi, A Wienhard, Surface group representations with maximal Toledo invariant, Ann. of Math. 172 (2010) 517 MR2680425
13	L Carvajales, Counting problems for special-orthogonal Anosov representations, Ann. Inst. Fourier (Grenoble) 70 (2020) 1199 MR4117059
14	J L Clerc, B Ørsted, The Maslov index revisited, Transform. Groups 6 (2001) 303 MR1870049
15	B Collier, N Tholozan, J Toulisse, The geometry of maximal representations of surface groups into SO₀(2,n), Duke Math. J. 168 (2019) 2873 MR4017517
16	J Danciger, F Guéritaud, F Kassel, Convex cocompactness in pseudo-Riemannian hyperbolic spaces, Geom. Dedicata 192 (2018) 87 MR3749424
17	J Danciger, F Guéritaud, F Kassel, Proper affine actions for right-angled Coxeter groups, Duke Math. J. 169 (2020) 2231 MR4139042
18	S Dey, M Kapovich, Patterson–Sullivan theory for Anosov subgroups, Trans. Amer. Math. Soc. 375 (2022) 8687 MR4504651
19	A Douady, J Oesterlé, Dimension de Hausdorff des attracteurs, C. R. Acad. Sci. Paris Sér. A-B 290 (1980) 1135 MR585918
20	L C Evans, R F Gariepy, Measure theory and fine properties of functions, CRC (2015) MR3409135
21	K J Falconer, The Hausdorff dimension of self-affine fractals, Math. Proc. Cambridge Philos. Soc. 103 (1988) 339 MR923687
22	H Federer, Geometric measure theory, 153, Springer (1969) MR0257325
23	O Glorieux, D Monclair, Regularity of limit sets of AdS quasi-Fuchsian groups, preprint (2018) arXiv:1809.10639
24	O Glorieux, D Monclair, Critical exponent and Hausdorff dimension in pseudo-Riemannian hyperbolic geometry, Int. Math. Res. Not. 2021 (2021) 13661 MR4320794
25	O Glorieux, D Monclair, N Tholozan, Hausdorff dimension of limit sets for projective Anosov representations, preprint (2019) arXiv:1902.01844
26	O Guichard, A Wienhard, Topological invariants of Anosov representations, J. Topol. 3 (2010) 578 MR2684514
27	O Guichard, A Wienhard, Positivity and higher Teichmüller theory, from: "European Congress of Mathematics" (editors V Mehrmann, M Skutella), Eur. Math. Soc. (2018) 289 MR3887772
28	O Hamlet, M B Pozzetti, Classification of tight homomorphisms, preprint (2014) arXiv:1412.6398
29	Harish-Chandra, Representations of semisimple Lie groups, VI : Integrable and square-integrable representations, Amer. J. Math. 78 (1956) 564 MR82056
30	J E Humphreys, Linear algebraic groups, 21, Springer (1975) MR0396773
31	J L Kaplan, J A Yorke, Chaotic behavior of multidimensional difference equations, from: "Functional differential equations and approximation of fixed points" (editors H O Peitgen, H O Walther), Lecture Notes in Math. 730, Springer (1979) 204 MR547989
32	I Kapovich, N Benakli, Boundaries of hyperbolic groups, from: "Combinatorial and geometric group theory" (editors S Cleary, R Gilman, A G Myasnikov, V Shpilrain), Contemp. Math. 296, Amer. Math. Soc. (2002) 39 MR1921706
33	M Kapovich, B Leeb, J Porti, Morse actions of discrete groups on symmetric space, preprint (2014) arXiv:1403.7671
34	M Kapovich, B Leeb, J Porti, A Morse lemma for quasigeodesics in symmetric spaces and Euclidean buildings, Geom. Topol. 22 (2018) 3827 MR3890767
35	F Labourie, Anosov flows, surface groups and curves in projective space, Invent. Math. 165 (2006) 51 MR2221137
36	F Ledrappier, Structure au bord des variétés à courbure négative, Sémin. Théor. Spectr. Géom. 13 (1995) 97 MR1715960
37	G Mess, Lorentz spacetimes of constant curvature, Geom. Dedicata 126 (2007) 3 MR2328921
38	R Potrie, A Sambarino, Eigenvalues and entropy of a Hitchin representation, Invent. Math. 209 (2017) 885 MR3681396
39	M B Pozzetti, A Sambarino, A Wienhard, Conformality for a robust class of non-conformal attractors, J. Reine Angew. Math. 774 (2021) 1 MR4250471
40	J F Quint, Cônes limites des sous-groupes discrets des groupes réductifs sur un corps local, Transform. Groups 7 (2002) 247 MR1923973
41	J F Quint, Divergence exponentielle des sous-groupes discrets en rang supérieur, Comment. Math. Helv. 77 (2002) 563 MR1933790
42	J F Quint, Mesures de Patterson–Sullivan en rang supérieur, Geom. Funct. Anal. 12 (2002) 776 MR1935549
43	J F Quint, An overview of Patterson–Sullivan theory, (2006)
44	A Sambarino, Hyperconvex representations and exponential growth, Ergodic Theory Dynam. Systems 34 (2014) 986 MR3199802
45	A Sambarino, The orbital counting problem for hyperconvex representations, Ann. Inst. Fourier (Grenoble) 65 (2015) 1755 MR3449196
46	D Sullivan, The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 171 MR556586
47	J Tits, Représentations linéaires irréductibles d’un groupe réductif sur un corps quelconque, J. Reine Angew. Math. 247 (1971) 196 MR277536
48	T Zhang, A Zimmer, Regularity of limit sets of Anosov representations, preprint (2019) arXiv:1903.11021