List of Publications (see also ArXiv, MathSciNet or Google Scholar)
S. Luzzatto, D. Veconi, K. War
Finite Time Hyperbolic Coordinates
Preprint (2025) (arxiv.org/abs/2502.00291arxiv.org/abs/2502.00291)
Finite Time Hyperbolic Coordinates
Preprint (2025) (arxiv.org/abs/2502.00291arxiv.org/abs/2502.00291)
J.F. Alves, D. Gama, S. Luzzatto
Statistical stability of interval maps with critical points and singularities
Journal of Dynamics and Differential Equations (2024) (ArXiv)
Statistical stability of interval maps with critical points and singularities
Journal of Dynamics and Differential Equations (2024) (ArXiv)
D. Coates, S. Luzzatto
Persistent Non-Statistical Dynamics in One-Dimensional Maps
Communication in Mathematical Physics (2024) (ArXiv)
Persistent Non-Statistical Dynamics in One-Dimensional Maps
Communication in Mathematical Physics (2024) (ArXiv)
D. Coates, S. Luzzatto, M. Mubarak
Doubly Intermittent Full Branch Maps with Critical Points and Singularities
Communication in Mathematical Physics (2023) (ArXiv)
Doubly Intermittent Full Branch Maps with Critical Points and Singularities
Communication in Mathematical Physics (2023) (ArXiv)
V. Climenhaga, S. Luzzatto, Y, Pesin.
SRB measures and Young towers for surface diffeomorphisms
Ann. Henri Poincaré 23, 973–1059 (2022). (ArXiv, Journal, Sharedit)
SRB measures and Young towers for surface diffeomorphisms
Ann. Henri Poincaré 23, 973–1059 (2022). (ArXiv, Journal, Sharedit)
A. Golmakani, C. E. Koudjinan, S. Luzzatto, P. Pilarczyk
Rigorous numerics for the quadratic family
Chaos 30, 073143 (2020) (ArXiv, Journal)
Rigorous numerics for the quadratic family
Chaos 30, 073143 (2020) (ArXiv, Journal)
S. Luzzatto, S. Tureli, K. War.
Integrability of Continuous Bundles
Journal für die reine und angewandte Mathematik (Crelle's Journal) 752 (2019) (ArXiv, Journal)
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)
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)
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)
Integrability of dominated decompositions on three dimensional manifolds
Ergodic Theory & Dynamical Systems, 37, no. 2 (2017) 606-620 (pdf, journal)
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)
A Frobenius Theorem for Corank-1 Continuous Distributions in Dimensions 2 and 3.
International Journal of Mathematics 27 (2016) no. 8 (ArXiv, Journal)
S Luzzatto, M. Ruziboev
Young Towers for Product Systems
Discrete and Continous Dynamical Systems, 36-3 (2016) 1465 - 1491
(ArXiv, Journal)
Young Towers for Product Systems
Discrete and Continous Dynamical Systems, 36-3 (2016) 1465 - 1491
(ArXiv, Journal)
S. Luzzatto, S. Tureli, K. War.
Integrability of C1 invariant splittings
Dynamical Systems: An International Journal. 31-1 (2016). (arXiv, journal)
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)
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)
Statistical properties and decay of correlations for interval maps with critical points and singularities.
Communications in Mathematical Physics 320 (2013) 21-35 (pdf)
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)
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)
Geometry of absolutely continuous expanding measures and the liftability problem
Ann. Inst. H. Poincaré Anal. Non Linéaire. 30 (2013) 101-120. (pdf)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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
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)
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)
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)
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)
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)
S. Luzzatto, I. Melbourne, F. Paccaut.
The Lorenz attractor is mixing.
Communication in Mathematical Physics, 260 (2005), pp. 393-401. (pdf)
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)
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)
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)
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)
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)
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)
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)
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)