Publications

Research articles

Proceedings, book chapters, etc

Research.

38 Banach spaces for piecewise cone hyperbolic maps (with S. Gouëzel) (2009) Preprint HAL+arxiv.org, submitted for publication

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 Published version (Copyright Cambridge University Press)

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

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. published arxiv version

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: C∞ foliations, in: Algebraic and Topological Dynamics", Sergiy Kolyada, Yuri Manin & Tom Ward (eds). Contemporary Mathematics, Amer. Math. Society, (2005) 123-136

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.

v Linear response despite critical points , Nonlinearity 21 T81-T90 (2008)

u Dynamics beyond uniform hyperbolicity: Linear response in the absence of structural stability , to appear Proceedings Equadiff 2007

t 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)

s 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. (Preliminary version: Course given at IHP workshop , 2005)

r Distributional analyses of Euclidean algorithms (with B. Vallée) Proceedings ANALCO04 pp 170-184

q 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)

p Stretched exponential bounds for the correlations of the Viana-Alves skew product (with S. Gouëzel) preprint 2002

o Kneading determinants and transfer operators in higher dimensions, ( Erratum ) Mandelbrot Jubilee, Proceedings of Symposia in Pure Mathematics, Amer. Math. Soc., Vol. 72,part. 2, pp. 407-417, 2004 (AMS-SMF conference Lyons 2001)

n Dynamical zeta functions and kneading operators, Course notes, New Directions in Dynamical Systems, Kyoto, 2002,

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) - Erratum

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) (Postscript file also available without figures )

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)