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Closed geodesics with prescribed intersection numbers

Yann Chaubet

Geometry & Topology 28 (2024) 701–758
Bibliography
1 N Anantharaman, Precise counting results for closed orbits of Anosov flows, Ann. Sci. École Norm. Sup. 33 (2000) 33 MR1743718
2 D V Anosov, Geodesic flows on closed Riemann manifolds with negative curvature, 90, Amer. Math. Soc. (1969) MR242194
3 M F Atiyah, R Bott, A Lefschetz fixed point formula for elliptic complexes, I, Ann. of Math. 86 (1967) 374 MR0212836
4 V Baladi, M F Demers, On the measure of maximal entropy for finite horizon Sinai billiard maps, J. Amer. Math. Soc. 33 (2020) 381 MR4073865
5 V Baladi, M F Demers, C Liverani, Exponential decay of correlations for finite horizon Sinai billiard flows, Invent. Math. 211 (2018) 39 MR3742756
6 F Bonahon, Bouts des variétés hyperboliques de dimension 3, Ann. of Math. 124 (1986) 71 MR0847953
7 F Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math. 92 (1988) 139 MR0931208
8 Y Bonthonneau, Les résonances du Laplacien sur les variétés à pointes, PhD thesis, Université Paris Sud (2015)
9 R Bowen, The equidistribution of closed geodesics, Amer. J. Math. 94 (1972) 413 MR0315742
10 R Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973) 429 MR0339281
11 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
12 F Dal’bo, Remarques sur le spectre des longueurs d’une surface et comptages, Bol. Soc. Brasil. Mat. 30 (1999) 199 MR1703039
13 N V Dang, G Rivière, Poincaré series and linking of Legendrian knots, preprint (2020) arXiv:2005.13235
14 H Delange, Généralisation du théorème de Ikehara, Ann. Sci. École Norm. Sup. 71 (1954) 213 MR0068667
15 S Dyatlov, C Guillarmou, Pollicott–Ruelle resonances for open systems, Ann. Henri Poincaré 17 (2016) 3089 MR3556517
16 S Dyatlov, M Zworski, Dynamical zeta functions for Anosov flows via microlocal analysis, Ann. Sci. Éc. Norm. Supér. 49 (2016) 543 MR3503826
17 V Erlandsson, J Souto, Counting curves in hyperbolic surfaces, Geom. Funct. Anal. 26 (2016) 729 MR3540452
18 C Guillarmou, Lens rigidity for manifolds with hyperbolic trapped sets, J. Amer. Math. Soc. 30 (2017) 561 MR3600043
19 V Guillemin, Lectures on spectral theory of elliptic operators, Duke Math. J. 44 (1977) 485 MR0448452
20 V Guillemin, A Pollack, Differential topology, Prentice-Hall (1974) MR348781
21 L Guillopé, Sur la distribution des longueurs des géodésiques fermées d’une surface compacte à bord totalement géodésique, Duke Math. J. 53 (1986) 827 MR0860674
22 G Higman, B H Neumann, H Neumann, Embedding theorems for groups, J. London Math. Soc. 24 (1949) 247 MR0032641
23 L Hörmander, The analysis of linear partial differential operators, I : Distribution theory and Fourier analysis, 256, Springer (1990) MR1065993
24 A Katsuda, T Sunada, Homology and closed geodesics in a compact Riemann surface, Amer. J. Math. 110 (1988) 145 MR0926741
25 Y Kifer, Large deviations, averaging and periodic orbits of dynamical systems, Comm. Math. Phys. 162 (1994) 33 MR1272765
26 S P Lalley, Closed geodesics in homology classes on surfaces of variable negative curvature, Duke Math. J. 58 (1989) 795 MR1016446
27 S P Lalley, Renewal theorems in symbolic dynamics, with applications to geodesic flows, non-Euclidean tessellations and their fractal limits, Acta Math. 163 (1989) 1 MR1007619
28 S P Lalley, Self-intersections of closed geodesics on a negatively curved surface: statistical regularities, from: "Convergence in ergodic theory and probability" (editors V Bergelson, P March, J Rosenblatt), Ohio State Univ. Math. Res. Inst. Publ. 5, de Gruyter (1996) 263 MR1412610
29 J M Lee, Riemannian manifolds: an introduction to curvature, 176, Springer (1997) MR1468735
30 R C Lyndon, P E Schupp, Combinatorial group theory, 89, Springer (1977) MR577064
31 G A Margulis, Certain applications of ergodic theory to the investigation of manifolds of negative curvature, Funkcional. Anal. i Priložen. 3 (1969) 89 MR0257933
32 M Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces, Ann. of Math. 168 (2008) 97 MR2415399
33 M Mirzakhani, Counting mapping class group orbits on hyperbolic surfaces, preprint (2016) arXiv:1601.03342
34 J P Otal, Le spectre marqué des longueurs des surfaces à courbure négative, Ann. of Math. 131 (1990) 151 MR1038361
35 W Parry, M Pollicott, An analogue of the prime number theorem for closed orbits of Axiom A flows, Ann. of Math. 118 (1983) 573 MR0727704
36 W Parry, M Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, 187–188, Soc. Math. France (1990) 268 MR1085356
37 F Paulin, M Pollicott, B Schapira, Equilibrium states in negative curvature, 373, Soc. Math. France (2015) MR3444431
38 R Phillips, P Sarnak, Geodesics in homology classes, Duke Math. J. 55 (1987) 287 MR0894581
39 M Pollicott, Asymptotic distribution of closed geodesics, Israel J. Math. 52 (1985) 209 MR0815810
40 M Pollicott, Homology and closed geodesics in a compact negatively curved surface, Amer. J. Math. 113 (1991) 379 MR1109342
41 M Pollicott, R Sharp, Angular self-intersections for closed geodesics on surfaces, Proc. Amer. Math. Soc. 134 (2006) 419 MR2176010
42 T Roblin, Ergodicité et équidistribution en courbure négative, 95, Soc. Math. France (2003) MR2057305
43 P C Sarnak, Prime geodesic theorems, PhD thesis, Stanford University (1980) MR2630950
44 Y G Sinai, Dynamical systems with elastic reflections: ergodic properties of dispersing billiards, Uspehi Mat. Nauk 25 (1970) 141 MR274721
45 I M Singer, J A Thorpe, Lecture notes on elementary topology and geometry, Scott, Foresman and Co (1967) MR213982