Publications Publications of Carlangelo Liverani (some downloadable in gz-compressed postscript or pdf format, with abstracts)

  1. Piecewise Contractions, with Sakshi Jain. To appear in Ergodic Theory and Dynamical Systems. Preprint Arxiv arXiv:2404.02371.
  2. Mean field coupled dynamical systems: Bifurcations and phase transitions, with Wael Bahsoun. Preprint Arxiv arXiv:2402.11076.
  3. Heat equation from a deterministic dynamics, with Giovanni Canestrari, and Stefano Olla. Preprint Arxiv arXiv:2310.13338.
  4. Projective Cones for Generalized Dispersing Billiards, with Mark Demers. Communication in Mathematical Physics, 401 (2023), no. 1, 841--923. Preprint arXiv:2104.06947.
  5. Globally coupled Anosov diffeomorphisms: Statistical properties, with Wael Bahsoun and Fanni M. Sélley. Communication in Mathematical Physics, 400 (2023), no. 3, 1791--1822. Preprint arXiv:2208.02517.
  6. Quantitative statistical properties of two-dimensional partially hyperbolic systems, with Roberto Castorrini. Advances in Mathematics, 409, Part A, 1-122 (2022) https://doi.org/10.1016/j.aim.2022.108625. Preprint arXiv:2007.05602
  7. Anosov diffeomorphisms, anisotropic BV spaces and regularity of foliations, with Wael Bahsoun. Ergodic Theory and Dynamical Systems, 42, 2431-2467 (2022). Preprint arXiv:2003.06811.
  8. Locating Ruelle-Pollicott resonances, with Oliver Butterley and Niloofar Kiamari. Nonlinearity, 35, (2022), 513-566. Preprint arXiv:2012.13145.
  9. Transfer operators in Hyperbolic Dynamics An introduction, with Mark Demers and Niloofar Kiamari. 33 Colloquio Brasilero de Matematica. Brazilian Mathematics Colloquiums sereis, Editora do IMPA. pp.252 (2021). ISBN 978-65-89124-26-9.
  10. Mixing rates for symplectic almost Anosov maps, with Peyman Eslami. Nonlinearity, 34, Number 6, (2021) pp. 3709--3731. Preprint arXiv:2003.07551.
  11. Edgeworth expansions for weakly dependent random variables, with Kasun Fernando. Annales de l'Institut Henri Poincarè Probability and Statstics, volume 57, number 1 (2021) 469--505. Preprint arXiv:1803.07667.
  12. Deterministic walks in random environment, with R.Aimino. Annals of Probability, Volume 48, Number 5 (2020), 2212-2257. Preprint ArXiv:1804.11114.
  13. Parabolic dynamics and Anisotropic Banach spaces with Paolo Giulietti. J. Eur. Math. Soc. (JEMS) 21, no. 9, 2793--2858 (2019).
  14. Transport in partially hyperbolic fast-slow systems. Proceedings of the International Congress of Mathematicians--Rio de Janeiro 2018. Vol. III. Invited lectures, 2629-2654 Talk to the ICM 2018. Preprint arXiv:1803.06137.
  15. Limit Theorems for Fast-slow partially hyperbolic systems with Jacopo De Simoi. Inventiones, pp. 1-206 (2018) Online version. DOI 10.1007/s00222-018-0798-9. Preprint arXiv:1408.5453.
  16. Exponential Decay of Correlations for Finite Horizon Sinai Billiard Flows with Viviane Baladi and Mark Demers. Inventiones, 211, 1, pp. 39--177 (2018). DOI 10.1007/s00222-017-0745-1. Preprint arXiv:1506.02836.
  17. Spectral properties of integral operators in bounded, large intervals, with Enza Orlandi. Journal of Mathematical Analysis and Applications, Volume 450, Issue 1, (2017) Pages 330-350. Preprint arXiv:1411.5221
  18. Fast-slow partially hyperbolic systems versus Friedlin--Wentzell random systems with Jacopo de Simoi, Christophe Poquet, Denis Volk. Journal of Statistical Physics, Volume 166, Issue 3 (2017) pp 650--679. DOI 10.1007/s10955-016-1628-3. Preprint arXiv:1607.04319.
  19. Statistical properties of mostly contracting fast-slow partially hyperbolic systems. with Jacopo De Simoi. Inventiones. 206, 1, (2016) 147--227, DOI 10.1007/s00222-016-0651-y Preprint. arXiv:1408.5454
  20. Mixing for some non-uniformly hyperbolic systems with Dalia Terhesiu. Abstract Annales Henri Poincarè, 17, (2016), 179-226. arXiv:1308.2422v2.
  21. The Martingale approach after Varadhan and Dolpogpyat with Jacopo De Simoi. In "Hyperbolic Dynamics, Fluctuations and Large Deviations", Dolgopyat, Pesin, Pollicott, Stoyanov editors, Proceedings of Symposia in Pure Mathematics, 89, AMS (2015). arXiv:1402.0090.
  22. Green-Kubo formula for weakly coupled systems with dynamical noise with Cedric Bernardin, Francois Huveneers, Joel Lebowitz and Stefano Olla. Communications in Mathematical Physics, 334 (2015), no. 3, 1377--1412. arXiv:1311.7384.
  23. Robustly invariant sets in fibre contracting bundle flows with O. Butterley. Journal of Modern Dynamics, 7, 2 (2013) 153-208. arXiv:1210.3791v1. Abstract
  24. A footnote on Expanding maps. Discrete and Continuous Dynamcial Systems, 33, 8, (2013) 3741--3751. arXiv:1207.3982v3. Abstract
  25. Anosov Flows and Dynamical Zeta Functions with Paolo Giulietti and Mark Pollicott. Annals of Mathematics, 178, 2 (2013) 687--773. arXiv:1203.0904v1. Abstract
  26. Multidimensional expanding maps with singularities: a pedestrian approach. Ergodic Theory and Dynamical Systems, 33 (2013) Pages 168--182. DOI:10.1017/S0143385711000939. arXiv:1110.2001v1.
  27. Exponential decay of correlations for piecewise cone hyperbolic contact flows with Viviane Baladi. Communications in Mathematical Physics, Volume 314, Number 3 (2012) Pages 689-773. DOI: 10.1007/s00220-012-1538-4. arXiv:1105.0567v2. Abstract
  28. Toward the Fourier law for a weakly interacting anharmonic crystal with Stefano Olla, Journal of the American Mathematical Society, 25 (2012) 555-583. arXiv:1006.2900v1. Abstract
  29. Energy transfer in a fast-slow Hamiltonian system with Dmitry Dolgopyat, Communications in Mathematical Physics, Volume 308, Number 1, 201-225 (2011). Abstract
  30. Heat equation from microscopic dynamics: a weak coupling approach, XVIth International Congress on Mathematical Physics, 397--400, World Sci. Publ., Hackensack, NJ, 2010.
  31. On the work and vision of Dmitry Dolgopyat, Journal of Modern Dynamics, 4, n. 2 (2010) 211--225. Abstract
  32. Map Lattices coupled by collisions, with Gerhard Keller, Communications in Mathematical Physics, 291, Issue 2 (2009), 591--597. Abstract
  33. Rare events, escape rates and quasistationarity: some exact formulae, with Gerhard Keller, Journal of Statistical Physics, 135, Issue 3 (2009), Page 519-534. Abstract
  34. Non-perturbative approach to random walk in markovian environment, with Dmitry Dolgopyat, Electronic Communications in Probability, 14 (2009), 245-251. Abstract
  35. Quenched CLT for random toral automorphism, with Arvind Ayyer and Mikko Stenlund, Discrete and Continuos Dynamical Systems, 24, 2, 331-348 (2009). Abstract
  36. Random Walk in Deterministically Changing Environment, with Dmitry Dolgopyat, ALEA 4, 89-116 (2008). Abstract
  37. Random Walk in Markovian Environment, with Dmitry Dolgopyat and Gerhard Keller, Annals of Probability, 36, Number 5 (2008), 1676-1710. Abstract
  38. Stability of Statistical Properties in Two-dimensional Piecewise Hyperbolic Maps, with Mark F. Demers, Transactions of the American Mathematical Society 360 (2008), 4777-4814. Abstract
  39. Compact locally maximal hyperbolic sets for smooth maps: fine statistical properties, with Sebastien Gouezel, Journal of Differential Geometry, 79 (2008) 433-477. Abstract
  40. Random Classical Fidelity, with Ph. Marie and S.Vaienti, Journal of Statistical Physics, 128, n. 4, (2007) 1079-1091. Abstract
  41. Smooth Anosov flows: correlation spectra and stability, with Oliver Butterley, Journal of Modern Dynamics, 1, 2, (2007) 301-322. Abstract
  42. Zeta functions and Dynamical Systems, with Masato Tsujii, Nonlinearity, 19, No 10 (October 2006) 2467-2473. Abstract
  43. Special Issue on Ergodic Theory and Non-uniform Dynamical Systems Guest Editor with Xavier Bressaud, Yves Lacroix, and Sandro Vaienti, Discrete and Continuous Dynamical Systems - Series A, 15, 1, (2006).
  44. Uniqueness of the SRB measure for piecewise expanding weakly coupled map lattices in any dimension, with G.Keller, Communications in Mathematical Physics, 262, 1, 33--50, (2006). Abstract
  45. Banach spaces adapted to Anosov systems, with S.Gouezel, Ergodic Theory and Dynamical Systems, 26, 1, 189--217, (2006). Abstract.
    This paper contains an imprecision. Please see this correction.
  46. Convergence to equilibrium for intermittent symplectic maps, with M.Martens, Communications in Mathematical Physics, 260, n.3, pp. 527--556 (2005). Abstract
  47. A spectral gap for a one-dimensional lattice of coupled piecewise expanding interval maps, with G.Keller, in "Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems", J.Chazottes and B.Fernandez Eds., Lecture Notes in Physics, Vol. 671, pp. 115--151, Springer (2005) Abstract
  48. Fredholm determinants, Anosov maps and Ruelle resonances, Discrete and Continuous Dynamical Systems, 13, 5, 1203-1215 (2005) Abstract
  49. Coupled map lattices without cluster expansion, with G.Keller, Discrete and Continuous Dynamical Systems, 11, n.2,3, 325--335 (2004). Abstract
  50. On Contact Anosov flows, Annals of Mathematics, 159, 3, 1275--1312 (2004) Abstract
  51. Birth of an elliptic island in a chaotic sea, Mathematical Physics Electronic Journal, 10, 1 (2004). Abstract
  52. Statistical properties of disordered quantum systems, with F.Fidaleo, Operator Theory: Advances and Applications, Vol. 153, Proceedings of the XIXth International Conference on Operator Theory, Timisoara (Romania), 2002; D.Gaspar. I.Gohberg, D.Timotin, F.H.Vasilescu and L.Zsido editors, Birkhauser Verlag Basel, Switzerland, pp. 123-141 (2004) Abstract
  53. Invariant measures and their properties. A functional analytic point of view, Dynamical Systems. Part II: Topological Geometrical and Ergodic Properties of Dynamics. Pubblicazioni della Classe di Scienze, Scuola Normale Superiore, Pisa. Centro di Ricerca Matematica "Ennio De Giorgi" : Proceedings. Published by the Scuola Normale Superiore in Pisa (2004). Abstract
  54. Ergodic properties of a model related to disordered quantum anharmonic crystals, with F.Fidaleo, Communications in Mathematical Physics, 235, 169-189 (2003). Abstract
  55. Lasota-Yorke maps with holes: conditionally invariant probability measures and invariant probability measures on the survivor set, with V. Maume-Deschamps, Annales de l'Institut Henri Poincarè Probability and Statistics, 39 (3), 385-412 (2003). Abstract
  56. Computing the rate of decay of correlations in expanding and hyperbolic systems , Markov Processes and Related Fields, 8, n.2, pp. 155-162 (2002). Abstract
  57. Ruelle-Perron-Frobenius spectrum for Anosov maps, with M.Blank and G.Keller, Nonlinearity, 15, n.6, pp. 1905-1973 (2002). Abstract
  58. Anosov diffeomorphism and coupling, with X. Bressaud, Ergodic Theory and Dynamical Systems, 22, n. 1, pp. 129--152, (2002). Abstract
  59. Return to equilibrium in classical and quantum systems, in "Long Tine Behaviour of Classical and Quantum Systems" S. Graffi and A. Martinez edts, Series on Concrete and Applicable Mathematics Vol. 1, World Scientific, Singapore, pp. 1-32 (2001) Abstract
  60. Rigorous numerical investigation of the statistical properties of piecewise expanding maps--A feasibility study, Nonlinearity, 14, n. 3, pp. 463--490, (2001). Abstract
  61. Interacting particles, in ``Hard Balls Systems and the Lorentz gas" edit by D.Szasz, Springer series Encyclopaedia of Mathematical Sciences, 101, Springer, New York, (2000). Abstract.
  62. Ergodic properties for a quantum non linear dynamics , with Francesco Fidaleo, Journal of Statistical Physics, 97, 5/6, pp. 957--1009 (1999). Abstract.
  63. Stability of the spectrum for transfer operators., with Gerhard Keller, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (4) Vol. XXVIII, pp. 141--152 (1999). Abstract.
  64. A Probabilistic Approach to Intermittency, with S.Vaienti and B.Saussol, Ergodic Theory and Dynamical Systems, 19, pp. 671--685 (1999). Abstract.
  65. Flows, Random Perturbations and Rate of Mixing, Ergodic Theory and Dynamical Systems, 18, 6, pp. 1421--1446 (1998). Abstract.
  66. Conformal Measure and Decay of Correlations for Covering Weighted Systems, with B. Saussol and S.Vaienti, Ergodic Theory and Dynamical Systems, 18, 6, pp. 1399--1420 (1998). Abstract.
  67. Conformally Symplectic Dynamics and Symmetry of the Lyapunov Spectrum, with M.Wojtkowski, Communications in Mathematical Physics, 194,1, pp. 7--60 (1998). Abstract.
  68. Reversibility in Infinite Hamiltonian Systems with Conservative Noise, with József Fritz and Stefano Olla, Communication in Mathematical Physics, 189, 2, pp. 481--496 (1997). Abstract.
  69. Central Limit Theorem for Deterministic Systems, International Conference on Dynamical Systems, Montevideo 1995, a tribute to Ricardo Mañ e, Pitman Research Notes in Mathemaics Series, 362, editori F.Ledrappier, J.Levovicz, S.Newhouse, (1996). Abstract.
  70. Ergodicity in Infinite Hamiltonian Systems with Conservative Noise, with S. Olla, Probability Theory and Related Fields, 106, pp. 401--445, (1996). Abstract.
  71. Decay of Correlations in Hyperbolic Systems , Proceedings of the International Conference on Dynamical Systems and Chaos--Tokyo 94, World Scientific Publ. Co., Singapore, pp. 163-166 (1995). Abstract.
  72. Decay of Correlations in Piecewise Expanding maps, Journal of Statistical Physics, 78, 3/4, pp. 1111-1129, (1995). Abstract.
  73. Decay of Correlations, Annals of Mathematics, 142, pp. 239-301, (1995). Abstract.
  74. Ergodicity in Hamiltonian Systems, with M. Wojtkowski, Dynamics Reported, 4, pp. 130-202, (1995). Abstract. Scanned version with figures (heavy)
  75. Generalization of the Hilbert Metric to the Space of Positive Definite Matrices, with M.Wojtkowski, Pacific Journal of Mathematics, 166 n. 2, pp. 339-355, (1994). Abstract.
  76. Ergodic Systems of n Balls in a Billiard Table, with L. Bunimovich, S. Pellegrinotti and Y.Suhov, Communications in Mathematical Physics, 146, pp. 357-396, (1992).
  77. Potential on the Two-Torus for which the Hamiltonian Flow is Ergodic, with V. Donnay, Communications in Mathematical Physics, 135, pp. 267--302, (1991).
  78. Dissipative Quantum Dynamics in a Boson Bath, with Y.-C. Chen, J.L. Lebowitz, Physical Review B, 40 , 7, pp. 4664--4682, (1989).
  79. Quantum System in Contact with a Thermal Environment: Rigorous Treatment of a Simple Model, with P. de Smet, D. Dürr, J.Lebowitz, Communications in Mathematical Physics, 120, pp. 195--231, (1988).
  80. Improved KAM Estimates for the Siegel Radius, with G. Turchetti, Journal of Statistical Physics, 45, 5/6, pp. 1071--1086, (1986).
  81. Some KAM Estimates for the Siegel Center Problem, with G. Servizi, G. Turchetti, Lettere al Nuovo Cimento, 39, pp. 417--423, (1984).
  82. Existence and Asymptotic Behavior of Pade` Approximants to the KdV Multisoliton Solutions, with G. Turchetti, Journal of Mathematical Physics, 24 , 1, pp. 53--64, (1983).
  83. Approximate Solutions of Some Solitonic Equations, Lettere al Nuovo Cimento, 34, 16, pp. 481--486, (1982).
  84. Approximate Solution of KdV Equation from Perturbation Expansion , with G. Turchetti, Lettere al Nuovo Cimento, 30, 1, p. 9, (1981).