Stefano Luzzatto Abdus Salam International Centre for Theoretical Physics (ICTP)
Strada Costiera 11
Trieste, Italy
luzzatto@ictp.it
+39 040 2240253
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Research Papers      (see also ArXiv, MathSciNet or Google Scholar)

A. Golmakani, C. E. Koudjinan, S. Luzzatto, P. Pilarczyk
Rigorous numerics for the quadratic family
Preprint ​(ArXiv)
V. Climenhaga, S. Luzzatto, Y, Pesin.
SRB measures and Young towers for surface diffeomorphisms
​Preprint (ArXiv)
S. Luzzatto, S. Tureli, K. War.
Integrability of Continuous Bundles
Journal für die reine und angewandte Mathematik (Crelle's Journal) 752 (2019)  (ArXiv, Journal)
Alves, J.F.; Dias, C.L.; Luzzatto, S. Pinheiro, V.  
SRB measures for partially hyperbolic systems whose central direction is weakly expanding. 

Journal of the European Mathematical Society, 19 (2017) no. 10, 2911-2946   (ArXiv, Journal) 
V. Climenhaga; S. Luzzatto; Y. Pesin
The geometric approach for constructing Sinai-Ruelle-Bowen measures
​Journal of Statistical Physics. ​27 (2017), no. 3-4, 467-493. (Journal)
S. Luzzatto, S. Tureli, K. War.
Integrability of dominated decompositions on three dimensional manifolds
Ergodic Theory & Dynamical Systems, 37, no. 2 (2017) 606-620 (pdf, journal)
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S. Luzzatto, S. Tureli, K. War.
A Frobenius Theorem for Corank-1 Continuous Distributions in Dimensions 2 and 3.
International Journal of Mathematics​ 27 (2016) no. 8 (ArXiv, Journal)

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S Luzzatto, M. Ruziboev
Young Towers for Product Systems
Discrete and Continous Dynamical Systems, 36-3 (2016) 1465 - 1491 
​(ArXiv, Journal)

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S. Luzzatto, S. Tureli, K. War.
Integrability of C1 invariant splittings
Dynamical Systems: An International Journal. 31-1 (2016). (arXiv,  journal)

A. Golmakani, S. Luzzatto, P. Pilarczyk
Uniform expansivity outside the critical neighborhood in the quadratic family
Experimental Mathematics, 25-2 (2016) (ArXiv, Journal)
S. Luzzatto,  I. Melbourne. 
Statistical properties and decay of correlations for interval maps with critical points and singularities. 
Communications in Mathematical Physics 320 (2013) 21-35  (pdf) 
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S. Luzzatto, F. J. Sanchez-Salas. 
Uniform hyperbolic approximation of measures with non-zero Lyapunov exponents. 
Proceedings of the AMS 141 (2013) 3157-3169  (pdf)
J.F. Alves, C. Dias, S. Luzzatto. 
Geometry of  absolutely continuous expanding measures and the liftability problem 
Ann. Inst. H. Poincaré Anal. Non Linéaire. 30 (2013) 101-120. (pdf) 
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F Alves, J.M. Freitas, S. Luzzatto, S. Vaienti, 
From rates of mixing to recurrence times via large deviations. 
Advances in Mathematics, 228 (2011), 1203-1236. (pdf)

Luzzatto, P. Pilarczyk. 
Finite resolution dynamics. 
Foundations of Computational Mathematics, Vol. 11, No. 2 (2011), 211-239 (pdf)
V. Araujo, S. Luzzatto, M. Viana. 
Invariant measures for interval maps with critical points and singularities. 
Advances in Mathematics pp. 1428-1444 (2009) (pdf)
K. Bloor, S. Luzzatto, 
Some remarks on the geometry of the standard map 
Int. J. Bif. Chaos pp 2213-2232 (2009) (pdf)
S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk. 
Quantitative hyperbolicity estimates in one-dimensional dynamics, 
Nonlinearity 21 (2008) 1967-1987 (pdf)
Y. Cao., S. Luzzatto, I. Rios. 
Hyperbolicity estimates for random maps with positive Lyapunov exponents. 
Proceedings of the AMS 136 (2008) 3591-3600. (pdf) 
Cao., S. Luzzatto, I. Rios. 
The boundary of hyperbolicity for Hénon-like families. 
Ergodic Theory and Dynamical Systems 4(2008) 1049-1080 (pdf)
M. Holland, S. Luzzatto. 
Stable manifolds under very weak hyperbolicity conditions. 
Journal of Differential Equations, 221, pp. 444-469 (2006) (pdf)
S. Luzzatto, H. Takahashi. 
Computable starting conditions for the existence of nonuniform hyperbolicity in one-dimensional maps. 
Nonlinearity 19, pp. 1657-1695 (2006). (pdf)
K. Diaz-Ordaz, M. Holland, S. Luzzatto. 
Decay of correlations for one-dimensional Lorenz-like maps with critical points and singularities. 
Stochastics and Dynamics, 6 (2006), no. 4, pp. 423-458 
Y. Cao. S. Luzzatto, I. Rios. 
A non-hyperbolic system with non-zero Lyapunov exponents for all invariant measures: internal tangencies. 
Discrete and Continuous Dynamical Systems, 15,pp. 61-71 (2006). (pdf)
S. Luzzatto, L. Wang. 
Topological invariance of generic non-uniformly expanding one-dimensional maps. 
Mathematical Research Letters, 13, pp. 343-357 (2006). (pdf)
H. Bruin, S. Luzzatto
Topological invariance of the sign of the Lyapunov exponents in one-dimensional maps. 
Proceedings of the AMS, 134 (2006), no. 1, pp. 265-272. (pdf)
J. F. Alves, S. Luzzatto, V. Pinheiro. 
Markov structures and decay of correlations for non-uniformly expanding maps. 
Annales de l’Institut Henri Poincare,  Analyse Non-Lineaire, 22 (2005), no. 6, pp. 817-839. (pdf)
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S. Luzzatto, I. Melbourne, F. Paccaut. 
The Lorenz attractor is mixing.
 Communication in Mathematical Physics, 260 (2005), pp. 393-401. (pdf)
Y. Cao., S. Luzzatto, I. Rios.
 A minimum principle for Lyapunov exponents and a higher dimensional version of a Theorem of Mané. 
Qualitative Theory of Dynamical Systems, 6, pp. 261-273 (2005). (pdf)
J. F. Alves, S. Luzzatto, V. Pinheiro. 
Lyapunov exponents and rates of mixing for one-dimensional maps. 
Ergodic Theory and Dynamical Systems 24 (2004) pp. 637—657 (pdf)
S. Luzzatto, M. Viana. 
Parameter exclusions in Hénon-like systems 
Russian Mathematical Surveys. 58 (2003) pp. 1053-1092 (pdf)
H. Bruin, S. Luzzatto, S. van Strien. 
Rates of decay of correlations for one-dimensional dynamics, 
Annales Scientifiques de l’École Normale Supérieure, 36 (2003), 621-646 (pdf)
S. Luzzatto, M. Viana. 
Positive Lyapunov exponents for a family of Lorenz-like maps with criticality's, 
Astérisque, 261 (2000), 201-237. (pdf)
S.Luzzatto, W. Tucker. 
Non-uniformly expanding dynamics in maps with criticalities and singularities. 
Publications Mathematiques IHES, 89 (1999), 179–226. (pdf)

Surveys, announcements and reports

S. Luzzatto, 
Stochastic-like behaviour in non-uniformly expanding maps. 
Handbook of Dynamical Systems, Vol. 1B, 265–326 B. Hasselblatt and A. Katok (Eds), Elsevier. (2006) (pdf)

M. Holland, S. Luzzatto. 
A new proof of the stable manifold theorem for hyperbolic fixed points on surfaces. 
Journal of Difference Equations & Applications, 11, pp. 535–551 (2005) (pdf)


J. F. Alves, S. Luzzatto, V. Pinheiro. 
Markov structures and decay of correlations for non-uniformly expanding maps on compact manifolds of arbitrary dimension. Electronic Research Announcements of the AMS, 9
(2003), pp 26-31. 


S. Luzzatto, 
Bounded recurrence of critical points and Jakobson’s Theorem 
The Mandelbrot set: themes and variations, Tan Lei (Editor), LMS Lecture Notes vol 274, CUP (2000). (pdf)


S. Luzzatto, 
Is philosophy detrimental to mathematics education? 
Philosophia Mathematica, Vol 6, pp. 65-72 (1991) (pdf)