"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 rentetive 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)

**50**
On the fractional susceptibility function of piecewise expanding maps
(with M. Aspenberg, J. Leppänen, and T. Persson,
(2019) arXiv and Hal preprint, submitted

**49**
There are no deviations for the ergodic averages of the Giulietti-Liverani horocycle flows
on the two-torus
(2019) arXiv and Hal preprint, to appear ETDS

**48**
On the measure of maximal entropy for finite horizon Sinai billiard maps
(with M. Demers)
(2018) arXiv and Hal,
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).

**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