"But a counter-current of recomposition is also at work. Even as the eye looks away momentarily from the written passage, even as the local unit of textual material - the word, the sentence, the paragraph, the stanza in the poem, the scene in the play, the chapter in the novel - is receding into more or less retentive recollection, an erosion towards unity occurs. The detail is made less distinct as it enters into a largely subconscious, provisional construct of the whole. A memory trained to art will include within itself the skills of forgetting; it will smooth the sharp edges of the particular as our fingers smooth the edge of the stone before inserting it in the mosaic." (G. Steiner, Antigones)

**53**
Horocycle averages on closed manifolds and transfer operators
(with A. Adam) (2021) arXiv and HAL, submitted for publication

**52**
Thermodynamic formalism for dispersing billiards
(with M. Demers)
(2020) arXiv and Hal, submitted

**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

In the "second fact" in the proof of Lemma 5.3 (when referring
to Thm 1.1 in [18]) the L_1 norm in the rhs should be a sup norm.

**50**
On the fractional susceptibility function of piecewise expanding maps
(with M. Aspenberg, J. Leppänen, and T. Persson),
DCDS (2021), 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 (2021),
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

As the result of [Bu] is only asymptotic, the
last lines of section 2.3 should be replaced by
"if h _* > s0 log 2, then there exists C > 0 and M>=2 so that
#Fix T^m >=Cexp(h _*m) for all m >= M [Bu, Theorem 1.5]".
Footnote 36 refers to the lower bound (7.26),
but it should instead refer to the upper bound (7.25).

Lemma 4.3 in Thermodynamic formalism for dispersing billiards (by the same
authors, see also Remark 4.4 there) showing that L_t(C^1) is contained in the Banach space
furnishes
the proof of Lemma 4.9 here, which had been
omitted.

**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

Minor corrections

**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.

3 comments

**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
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

Corrigendum (Nonlinearity 25 (2012) 2203-2205)
(The
end of the proof of Thm 7.1 is amended: the claim about dense
postscritical orbits is that "there exists a sequence" tn, not "for
all sequences")

**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:
* 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),
Corrigendum
2010 and 2017

**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)

**15**Sharp
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)

(Above Lemma 3.2, "by some M_γ" should be replaced by
"by M_γ φ(x) for some M_γ", the Hölder constant being local at x.)

**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)

**y**
Dynamical zeta functions and dynamical determinants for hyperbolic maps,
Springer Ergebnisse, 2018,
front and backmatter on Mittag-Leffler preprint server (Fractal Geometry
and Dynamics Program, Fall 2017) ,
Erratum

**x**
Dynamical zeta functions
Graduate course, Orsay, 2002

**w**
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

**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)
*

For preprints consult the
mp_archive
and
arXiv