56 Thermodynamic formalism for piecewise expanding maps in finite dimension (with R. Castorrini) DCDS 44 2169-2192 (2024) doi:10.3934/dcds.2024023
55 A parameter ASIP for the quadratic family (with M. Aspenberg and T. Persson) ETDS 45 663-703 (2025) doi.org/10.1017/etds.2024.67
54 Measure of maximal entropy for finite horizon Sinai billiard flows (with J. Carrand and M. Demers) Ann. H. Lebesgue 7 727-747 (2024) doi.org/10.5802/ahl.209
53
Horocycle averages on closed manifolds and transfer operators
(with A. Adam) Tunisian J. Math 4 387-441 (2022)
doi:10.2140/tunis.2022.4.387
52
Thermodynamic formalism for dispersing billiards
(with M. Demers)
J. Mod. Dynam. 18 415-493 (2022) doi:10.3934/jmd.2022013
51
Fractional susceptibility functions for the quadratic family: Misiurewicz-Thurston parameters
(with D. Smania),
Comm. Math. Phys. 385 1957-2007 (2021)
https://doi.org/10.1007/s00220-021-04015-z
50 On the fractional susceptibility function of piecewise expanding maps (with M. Aspenberg, J. Leppänen, and T. Persson), DCDS 42 (2022) 679-706, doi:10.3934/dcds.2021133
49 There are no deviations for the ergodic averages of the Giulietti-Liverani horocycle flows on the two-torus ETDS 42 Anatole Katok Memorial Issue Part 1 (2022) 500-513, https://doi.org/10.1017/etds.2021.17
48
On the measure of maximal entropy for finite horizon Sinai billiard maps
(with M. Demers)
JAMS 33 381-449 (2020), DOI:https://doi.org/10.1090/jams/939
47 Characteristic functions as bounded multipliers on anisotropic spaces Proceedings Amer. Math. Soc. 146 4405-4420 (2018) DOI: https://doi.org/10.1090/proc/14107
46 The quest for the ultimate anisotropic Banach space J. Stat. Phys. 166 525-557 (2017) (volume in honour of Ruelle and Sinai) (DOI) 10.1007/s10955-016-1663-0 (Corrections and complements) 170 1242-1247 (2018) /doi.org/10.1007/s10955-018-1976-2
45 Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables (with T. Kuna and V. Lucarini) Nonlinearity 30 1204-1220 (2017) DOI: 10.1088/1361-6544/aa5b13, Corrigendum Nonlinearity 30 C4-C6 (2017) doi.org/10.1088/1361-6544/aa7768
44 Linear response for intermittent maps (with M. Todd) Comm. Math. Phys. 347 857-874 (2016) DOI: 10.1007/s00220-016-2577-z
43
Exponential decay of correlations for finite horizon Sinai billiard flows
(with M. Demers and C. Liverani)
Invent. Math.
211 39-177 (2018) DOI 10.1007/s00222-017-0745-1
42
Whitney-Holder continuity of the SRB measure for transversal families of
smooth unimodal maps(with M. Benedicks and D. Schnellmann)
Invent. Math. 201 773-844 (2015) doi 10.1007/s00222-014-0554-8
41 Natural boundary for the susceptibility function of generic piecewise expanding unimodal maps (with S. Marmi and D. Sauzin) ETDS 34 (2014) 777-800 doi:10.1017/etds.2012.161
40 Exponential decay of correlations for piecewise cone hyperbolic contact flows (with C. Liverani) Comm. Math. Phys. 314 (2012) 689-773, (DOI) 10.1007/s00220-012-1538-4
39
Linear response for smooth deformations of generic nonuniformly
hyperbolic unimodal maps (with D.
Smania)
Ann. ENS 45 (2012) 861-926.
38 Banach spaces for piecewise cone hyperbolic maps (with S. Gouëzel) J. Modern Dynam., 4 (2010) 91-137
37 Alternative proofs of linear response for piecewise expanding unimodal maps (with D. Smania) (2010) Ergodic Theory Dynamical Systems 30 1-20 doi:10.1017/S0143385708001077
36 Analyticity of the SRB measure for holomorphic families of quadratic-like Collet-Eckmann maps (with D. Smania) Proc. Amer. Math. Soc. 137 (2009) 1431-1437
35 Good Banach spaces for piecewise hyperbolic maps via interpolation (with S. Gouëzel) Annales de l'Institut Henri Poincaré / Analyse non linéaire 26 (2009) 1453-1481 DOI: 10.1016/j.anihpc.2009.01.001
34 Smooth deformations of piecewise expanding unimodal maps, (with D. Smania) DCDS Series A 23 (2009) 685-703
33
Linear response formula for piecewise expanding unimodal maps,
(with D. Smania)
Nonlinearity , 21 (2008) 677-711
Corrigendum (Nonlinearity 25 (2012) 2203-2205)
32 On the susceptibility function of piecewise expanding interval maps, Comm. Math. Phys. 275 (2007) 839-859
31
Dynamical determinants and spectrum for hyperbolic diffeomorphisms,
(with M. Tsujii) pp. 29--68, in Probabilistic and Geometric Structures in Dynamics,
K. Burns, D. Dolgopyat and Ya. Pesin (eds),
Contemp. Math. 469 (Amer. Math. Soc.), Volume in honour of M.
Brin's 60th birthday (2008).
30 A local limit theorem with speed of convergence for euclidean algorithms and diophantine costs, (with A. Hachemi) Ann. I.H.P. prob. stat. 44 (2008) 749-770.
29 Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms, (with M. Tsujii) Ann. Inst. Fourier, 57 (2007) 127-154
28
Anisotropic Sobolev spaces and dynamical transfer operators:
27 Exponential decay of correlations for surface semi-flows without finite Markov partitions, (with B. Vallée) Proc. Amer. Math. Soc. , 133 (2005) 865-874
26 A note on stretched exponential decay of correlations for the Viana-Alves map, (with S. Gouëzel) Preprint, arXiv:math.DS/0311189 (2003)
25 Euclidean algorithms are Gaussian, (with B. Vallée) J. Number Theory , 110 (2005) 331-386
24 Dynamical zeta functions for analytic surface diffeomorphisms with dominated splitting, (with E. Pujals and M. Sambarino) J. Inst. Math. de Jussieu, 4 (2005) 175-218, copyright Cambridge University Press
23 Kneading determinants and spectra of transfer operators in higher dimensions, the isotropic case, (with M. Baillif) Ergodic Theory Dynam. Systems, 25 (2005) 1437-1470
22 Dynamical determinants via dynamical conjugacies for postcritically finite polynomials, (with H.-H. Rugh and Y. Jiang) J. Stat. Phys., 108, 973-993 (2002)
21 Floquet spectrum of weakly coupled map lattices, (with H.-H. Rugh) Comm. Math. Phys., 220, 561-582 (2001)
20 Almost sure rates of mixing for i.i.d. unimodal maps, (with M. Benedicks and V. Maume-Deschamps) Ann. E.N.S., 35 77-126 (2002); Corrigendum Ann. E.N.S., 36 319-322 (2003),
19 Approximation of nonessential spectrum of transfer operators, (with M. Holschneider) Nonlinearity, 12, 525-538 (1999)
18 The spectrum of weakly coupled map lattices, (with M. Degli Esposti, S. Isola, E. Järvenpää, and A. Kupiainen) Journal de Mathématiques Pures et Appliquées, 77, 539-584 (1998)
17 Abnormal escape rates from nonuniformly hyperbolic sets, (with C. Bonatti and B. Schmitt) Ergodic Theory Dynamical Systems, 19, 1111-1125 (1999)
16 Correlation spectrum of quenched and annealed equilibrium states for random expanding maps, Comm. Math. Phys., 186, 671-700 (1997)
15Sharp determinants and kneading operators for holomorphic maps (with A. Kitaev, D. Ruelle, and S. Semmes), Proc. Steklov Math. Inst. 216, 186-228 (1997)
14 Lyapunov exponents for non-classical multidimensional continued fraction algorithms (with A. Nogueira), Nonlinearity, 9, 1529-1546 (1996)
13
Random correlations for small
perturbations of expanding maps
(with A. Kondah and B. Schmitt),
Random & Comput. Dyn.,
4, 179-204 (1996)
12 Strong stochastic stability and rate of mixing for unimodal maps (with M. Viana), Ann. scient. Ec. norm. sup. (4) 29, 483-517 (1996)
11 Transfer operators acting on Zygmund functions (with Y. Jiang and O.E. Lanford III), Trans. Amer. Math. Soc. 348, 1599-1615 (1996)
10 Sharp determinants (with D. Ruelle), Invent. Math. 123, 553-574 (1996)
9 Transfer operators for piecewise affine approximations of interval maps (with S. Isola and B. Schmitt), Annales Inst. H. Poincaré (phys. théor.) 62, 251-266 (1995)
8 Infinite kneading matrices and weighted zeta functions of interval maps, J. Functional Analysis 128, 226-244 (1995)
7 An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps (with D. Ruelle), Ergodic Theory Dynamical Systems 14, 621-632 (1994)
6 On the spectra of randomly perturbed expanding maps (with L.-S. Young), Comm. Math. Phys 156, 355-385 (1993), Erratum, Comm. Math. Phys 166, 219-220 (1994)
5 Renormalization on the n-dimensional torus (with D. Rockmore, N. Tongring, and C. Tresser), Nonlinearity 5, 1111-1137 (1992)
4 Optimality of Ruelle's bound for the domain of meromorphy of generalized zeta functions, Portugaliae Mathematica 49, 69-83 (1992)
3 Gibbs states and equilibrium states for finitely presented dynamical systems, J. Stat. Phys. 62, 239-256 (1991)
2 Zeta functions and transfer operators for piecewise monotone transformations (with G. Keller), Comm. Math. Phys. 127, 459-479 (1990)
1 Resonances for intermittent systems (with J.-P. Eckmann and D. Ruelle), Nonlinearity 2, 119-135 (1989)
Conference proceedings, book chapters etc.
u Dynamical zeta functions and dynamical determinants for hyperbolic maps, Springer Ergebnisse, 2018.
t Linear response, or else Proceedings of the International Congress of Mathematicians-Seoul 2014. Vol. III. Invited lectures. 525-545. Papers from the congress (ICM 2014) held August 13-21, 2014. Edited by Sun Young Jang, Young Rock Kim, Dae-Woong Lee and Ikkwon Yie. Kyung Moon Sa, Seoul, 2014. vii+1250 pp. ISBN: 978-89-6105-806-3; 978-89-6105-803-2
s Linear response despite critical points, Nonlinearity 21 T81-T90 (2008)
r Regularisation for dynamical zeta functions, in Encyclopedia of Mathematical physics, ed. J-P Francoise, G. Naber, Sh. Tsun Tsou, Elsevier (2006) (Vol 4 pp 386-390)
q Spectra of differentiable hyperbolic maps (with M. Tsujii) in "Traces in number theory, geometry and quantum fields", S. Albeverio, M. Marcolli, S. Paycha (eds), Aspects of Mathematics E38, pp. 1-21, Vieweg Verlag 2008; proceedings MPIM Bonn 2005.
p Distributional analyses of Euclidean algorithms (with B. Vallée) Proceedings ANALCO04 pp 170-184
o Résonances dans les systèmes hyperboliques et hamiltoniens notes de cours, 2003 Resonances in hyperbolic and hamiltonian systems has appeared in "Harmonic analysis and rational approximation - an outgrowth of the 2003 Porquerolles summer school" Springer Lecture Notes in Control and Information Sciences, vol 327 (2006)
n Kneading determinants and transfer operators in higher dimensions, Mandelbrot Jubilee, Proceedings of Symposia in Pure Mathematics, Amer. Math. Soc., Vol. 72,part. 2, pp. 407-417, 2004 (AMS-SMF conference Lyons 2001)
m Finite-dimensional functional analysis applied to transfer operators for infinite-dimensional maps, Proceedings Journées Systèmes Aléatoires Inhomogènes, (January 2001, Université de Cergy-Pontoise, France), session on Rapidity of convergence to equilibrium or stationary states, Markov Processes and Related Fields, 8, 149-154 (2002).
l Spectrum and Statistical Properties of Chaotic Dynamics, Proceedings Third European Congress of Mathematics, 203-224 Barcelona 2000, Birkhauser (2001)
k Positive Transfer Operators and Decay of Correlations, Book Advanced Series in Nonlinear Dynamics, Vol 16, World Scientific, Singapore (2000)
j Decay of random correlation functions for unimodal maps, (with M. Benedicks and V. Maume-Deschamps) Proceedings 31st Symposium on Mathematical Physics, May 18-21 1999, Torun, Reports on Mathematical Physics, 46, 15-26 (2000)
i Decay of correlations, 1999 AMS Summer Institute on Smooth ergodic theory and applications, Seattle, Proc. Symposia in Pure Math. Vol. 69, AMS (2001), pp 297-325
h Periodic orbits and dynamical spectra, Ergodic Theory Dynamical Systems, 18, 255-292 (1998)
g The Magnet and the Butterfly: Thermodynamic formalism and the ergodic theory of chaotic dynamics, in: Développement des mathématiques au cours de la seconde moitié du XXe siècle, Birkhauser, Basel (2000)
f A brief introduction to dynamical zeta functions, in: DMV-Seminar 27, Classical Nonintegrability, Quantum Chaos, by A. Knauf and Ya.G. Sinai, Birkhäuser, 3-20 (1997)
e Dynamical zeta function and generalised Fredholm determinants (with a joint Appendix with D. Ruelle: Some properties of zeta functions associated with maps in one dimension), XIth International Congress of Mathematical Physics (Paris 1994), Internat. Press, Cambridge, 249-260 (1995)
d Dynamical zeta functions, Proceedings of the NATO ASI "Real and Complex Dynamical Systems" (1993), B. Branner and P. Hjorth, editors, Kluwer Academic Publishers, Dordrecht, 1-26 (1995)
c Comment compter avec les fonctions zêta?, Gazette des Mathématiciens, 47, 79-96 (1991)
b Fonctions zêta,
fonctions de corrélation et états d'équilibre
pour quelques systèmes dynamiques non Axiome A,
Ph.D Thesis, University of Geneva, 98 pages (1989)
a A program for
computing Puiseux expansions
(with J.-P. Guillement),
SIGSAM Bulletin 24, 33-41 (1990)
See also
arXiv