"All truths are easy to understand once they are discovered; the point is to discover them" - Galileo

"Simplicity is the ultimate sophistication" - Leonardo da Vinci

Publications 

[1] P. Varandas, Correlation decay and recurrence asymptotics for some robust nonuniformly hyperbolic maps,  Journal of Statistical Physics, 133 (2008) 813-839. |  Journal | Preprint |

[2] P. Varandas, Entropy and Poincaré recurrence from a geometrical viewpoint,  Nonlinearity, 22 (2009) 2365-2375. | Journal | Preprint |

[3] P. Varandas and M. Viana, Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps  Annalles de l’Institut Henri Poincaré - Analyse Non-Linéaire, 27 (2010) 555-593. | Journal | Preprint |

[4] M. Bessa and P. Varandas, On the entropy of incompressible three-dimensional flows, Qualitative Theory of Dynamical Systems, 10 (2011) 11-22. | Journal | Preprint |

[5] P. Varandas, Non-uniform specification and large deviations for weak Gibbs measures, Journal of Statistical Physics, 146 (2012) 330-358. | Journal | Preprint |

[6] V. Araújo and P. Varandas, Robust exponential decay of correlations for singular-flows, Communications in Mathematical Physics, 311 (2012) 215-246 & Errata 341:2 (2016) 729-731 | Journal | Errata | Preprint |

[7] J. Rousseau, P. Varandas and Y. Zhao, Entropy formulas for dynamical systems with mistakes, Discrete and Continuous Dynamical Systems - A, 32:12 (2012) 4391-4407. | Journal | Preprint |

[8] A. Castro and P. Varandas, Equilibrium states for non-uniformly expanding maps: decay of correlations and strong stability, Annalles de l’Institut Henri Poincaré - Analyse Non-Linéaire, 30:2 (2013) 225-249. | Journal | Preprint |

[9] P. Varandas and Y. Zhao,  Weak specification properties and large deviations for non-additive potentials, Ergodic Theory and Dynamical Systems, 35:3 (2015) 968-993. | Journal | Preprint |

[10] P. Varandas, Statistical properties of generalized Viana maps, Dynamical Systems, 29:2 (2014) 167-189. | Journal | Preprint |

[11] J. Rousseau, P. Varandas and B. Saussol) Exponential law for random subshifts of finite type, Stochastic Processes and their Applications, 124 (2014) 3260-3276. | Journal | Preprint |

[12] C. Lizana, V. Pinheiro and P. Varandas, Contribution to the ergodic theory of robustly transitive maps, Discrete and Continuous Dynamical Systems - A, .35 (2015) 353-365. |  Journal | Preprint |

[13] M. Bessa and P. Varandas, Trivial and simple spectrum for SL(2,R) cocycles with free base and fiber dynamics, Acta Mathematica Sinica, 31:7 (2015) 1113-1121. | Journal | Preprint |

[14] N. Sumi, P. Varandas and K. Yamamoto, Partial hyperbolicity and specification, Proceedings of the American Mathematical Society, 144:3 (2016) 1161–1170.  | Journal | Preprint |

[15] P. Varandas, A version of Kac's lemma for suspension flows, Stochastics and Dynamics 16:2, (2106)   | Journal | Preprint |

[16]  I. Melbourne and P. Varandas, A note on statistical properties for nonuniformly hyperbolic systems with slow contraction and expansion, Stochastics and Dynamics, 16:3 (2016)  | Journal | Preprint |

[17] V. Araújo, I. Melbourne and P. Varandas, Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 map, Communications in Mathematical Physics 340 (2015) 901–938.  | Journal | Preprint |

[18] T. Bomfim and P. Varandas, Multifractal analysis of the irregular set for almost-additive sequences via large deviations, Nonlinearity, 28 (2015) 3563-3585. | Journal | Preprint |

[19] M. Carvalho and P. Varandas, (Semi)continuity of the entropy of Sinai probability measures for partially hyperbolic diffeomorphisms, Journal of Mathematical Analysis and Applications, 434:2 (2016) 1123-1137.  | Journal | Preprint version

[20] V. Araújo, O. Butterley and P. Varandas, Open sets of Axiom A flows with exponentially mixing attractors, Proceedings of the American Mathematical Society 144 (2016) 2971-2984. & Corrigendum  146:11 (2018) 5013–5014.  | Journal | Corrigendum | Preprint |

[21]  P. Varandas and Y. Zhao, Weak Gibbs measures: convergence to entropy, topological and geometrical aspects, Ergodic Theory and Dynamical Systems, 37:7, (2017), 2313-2336.  | Journal | Preprint |

[22] T. Bomfim, A. Castro and P. Varandas,  Differentiability of thermodynamical quantities, Advances in Mathematics, 292 (2016), 478–528.  | Journal | Preprint |

[23] F. Rodrigues and P. Varandas, Specification properties for group actions and thermodynamics of expanding semigroups, Journal of Mathematical Physics 57, (2016) 052704   | Journal | Preprint |

[24] M. Carvalho, F. Rodrigues and P. Varandas, Semigroups actions of expanding maps, Journal of Statistical Physics 116: 1 (2017), 114-136.  | Journal | Preprint |

[25] M. Bessa, C. Ferreira, J. Rocha and P. Varandas, Generic Hamiltonian dynamics, Journal of Dynamics and Differential Equations, 29:1 (2017) 203-2018.   | Journal | Preprint |

[26] T. Bomfim, M. J. Torres and P. Varandas, Topological features of flows with the reparametrized gluing orbit property, Journal of Differential Equations, 262:8 (2017) 4292-4313  | Journal | Preprint |

[27] M. Bessa, J. Bochi, M. Cambraínha, C. Matheus, P. Varandas and D. Xu, Positivity of top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases, Buletin of the Brazilian Mathematical Society, 49:1 (2018) 73-87  | Journal | Preprint |

[28] X. Tian and P. Varandas, Topological entropy of level sets of empirical measures for non-uniformly expanding maps, Discrete and Continuous Dynamical Systems - A, 37:10 (2017) 5407-5431  | Journal | Preprint |

[29] T. Bomfim and P. Varandas, Multifractal analysis for weak Gibbs measures: from large deviations to irregular sets, Ergodic Theory and Dynamical Systems, 37: 1 (2017) 79-102  | Journal | Preprint |

[30] J. Rocha and P. Varandas, The centralizer of C^r generic diffeomorphisms at hyperbolic basic sets is trivial, Proceedings of the American Mathematical Society, 146:1 (2018) 247-260  | Journal | Preprint |

[31] J. Rocha and P. Varandas, On sensitivity to initial conditions and uniqueness of conjugacies for structurally stable diffeomorphisms, Nonlinearity, 31:293 (2018) 293-313   | Journal | Preprint |

[32] W. Bonomo and J. Rocha and P. Varandas, The centralizer of Komuro-expansive flows and expansive Rd actions, Mathematische Zeitschrift, 289:3 (2018)  1059-1088   | Journal | Preprint |

[33] M. Carvalho, F. Rodrigues and P. Varandas, Quantitative Poincaré recurrence for semigroup actions, Nonlinearity, 31:3 (2018) 864-886  | Journal | Preprint |

[34]  M. Bessa and J. Rocha and P. Varandas, Uniform hyperbolicity revisited: periodic points and equidimensional cycles, Dynamical Systems,  33:4 (2018) 691-707  | Journal | Preprint |

[35] M. Bessa, M. J. Torres and P. Varandas, On the periodic orbits, shadowing and strong transitivity of continuous flows, Nonlinear Analysis, 175 (2018) 191-209  | Journal | Preprint | Errata |

[36] M. Carvalho, F. Rodrigues and P. Varandas, A variational principle for free semigroup actions, Advances in Mathematics, 334 (2018) 450-487  | Journal | Preprint |

[37] A. Cruz and P. Varandas, SRB measures for partially hyperbolic attractors of endomorphisms, Ergodic Theory and Dynamical Systems, 40:6 (2020) 1545 - 1593 | Journal | Preprint |

[38] L. Backes, M. Poletti and P. Varandas, Simplicity of Lyapunov spectrum for linear cocycles over non-uniformly hyperbolic systems (with an Appendix by Y. Lima) Ergodic Theory and Dynamical Systems, 40:11 (2020) 2947-2969  | Journal | Preprint |

[39] T. Bomfim and P. Varandas, The gluing orbit property, uniform hyperbolicity and large deviation principles for semiflows, Journal of Differential Equations 267 (2019) 228–266  | Journal | Preprint |

[40] W. Bonomo and P. Varandas, A criterion for the triviality of the centralizer for flows and applications, Journal of Differential Equations 267:3 (2019) 1748-1766  | Journal | Preprint |

[41] I. Melbourne and P. Varandas, Convergence to a Lévy process in the Skorohod M1 and M2 topologies for nonuniformly hyperbolic systems, including billiards with cusps,  Communications in Mathematical Physics 375 (2020) 653–678   | Journal | Preprint |

[42] P. Varandas, On the cohomological class of fiber-bunched cocycles on semi simple Lie groups, Revista Matemática Iberoamericana 36:4 (2020) 1113-1132  | Journal | Preprint |

[43] A. Cruz, G. Ferreira and P. Varandas, Volume lemmas and large deviations for partially hyperbolic endomorphisms, Ergodic Theory and Dynamical Systems 41: 1 (2021  213 - 240 | Journal | Preprint |

[44] W. Bonomo and P. Varandas, C1-generic sectional Axiom A flows have only trivial symmetries, Portugaliae Mathematica, 76:1 (2019) 29-48   | Journal | Preprint |

[45] A. Castro, F. Rodrigues and P. Varandas, Stability and limit theorems for sequences of uniformly hyperbolic dynamics, Journal of Mathematical Analysis and Applications, 480 (2019) 123426  | Journal |  Preprint |

[46] A. Castro, F. Rodrigues and P. Varandas, Leafwise shadowing property for partially hyperbolic diffeomorphisms, Dynamical Systems, 35:2 (2020) 306–314  | Journal | Preprint |

[47] W. Bonomo, H. Lima and P. Varandas, The rotation sets of most volume preserving homeomorphisms on  Td  are stable, convex and rational polyhedrons, Israel Journal of Mathematics 243 (2021) 81-102.  | Journal | Preprint | Slides |

[48] H. Lima and P. Varandas, On the rotation sets of generic homeomorphisms on the torus Td, Ergodic Theory and Dynamical Systems 41 (2021) 2983-3022 | Journal | Preprint | 

[49] W. Bonomo and P. Varandas,  Continuous flows generate few homeomorphisms, Proceedings of the Edinburgh Mathematical Society, 63:4 (2020) 971-983  | Journal | Preprint |

[50] M. Morro, R. Sant'Anna and P. Varandas, Ergodic optimization for hyperbolic flows and Lorenz attractors, Annales Henri Poincaré, 21:10 (2020) 3253-3283  | Journal | Preprint | Slides |

[51] P. Jung, I. Melbourne,  F. Pène, P. Varandas and H.-K. Zhang, Necessary and sufficient condition for M2-convergence to a Lévy process for billiards with cusps at flat points, Stochastics and Dynamics, 21:5 (2021) 2150024  | Journal | Preprint |

[52] M. Carvalho, F. Rodrigues and P. Varandas, A variational principle for the metric mean dimension of free semigroup actions, Ergodic Theory and Dynamical Systems 42:1 (2022) 65-85  | Journal | Preprint |

[53] T. Bomfim, M. J. Torres and P. Varandas, The gluing orbit property and partial hyperbolicity, Journal of Differential Equations 272 (2021) 203–221   | Journal | Preprint |

[54] J. Rocha and P. Varandas, On C^0 centralizers of Anosov diffeos on the torus: algebraic and topological aspects, Fundamenta Mathematicae  258 (2022), 1-24  | Journal | Preprint |

[55] M. Carvalho , F. Rodrigues and P. Varandas, Generic homeomorphisms have full metric mean dimension, Ergodic Theory and Dynamical Systems 42:1 (2022) 40-64 | Journal |  Preprint |

[56] D. Daltro and P. Varandas, Exponential decay of correlations for Gibbs measures and semiflows over C^1+ piecewise expanding maps,  Annales Henri Poincaré, 22:7 (2021), 2137-2159  | Journal | Preprint |

[57] M. Stadlbauer, S. Suzuki and P. Varandas, Thermodynamic formalism for random non-uniformly expanding maps, Communications in Mathematical Physics 385 : 1 (2021) 369427  | Journal | Preprint |

[58] M. Bessa, M. J. Torres and P. Varandas, Topological aspects of incompressible flows, Journal of Differential Equations 293 (2021) 392-417 | Journal | Preprint |

[59] P. Varandas, Realization of rotation vectors for volume preserving homeomorphisms of the torus, Topological Methods in Nonlinear Analysis 60 (2022) 441-455 | Journal | Preprint |

[60] M. Carvalho and P. Varandas, Genericity of historic behavior for maps and flows, Nonlinearity 34:10 (2021) 7030-7044 | Journal | Preprint |

[61] T. Bomfim, R. Huo, P. Varandas and  Y. Zhao, Typical properties of ergodic optimization for asymptotically additive potentials,  Stochastics and Dynamics, 23: 1 (2023) 2250024 | Journal | Preprint|

[62] A. Lopes, S. Lopes and P. Varandas, Bayes posterior convergence for loss functions via almost additive thermodynamic formalism, Journal of Statistical Physics 186:35 (2022) | Journal | Preprint |

[63]  A. Biś, M Carvalho, M. Mendes and P. Varandas, A convex analysis approach to entropy functions, variational principles and equilibrium states, Communications in Mathematical Physics 394 (2022) 215–256 | Journal | Preprint  (Extended version) | Slides |

[64] M. Carvalho, F. Rodrigues and P. Varandas, Entropy inequalities for semigroups actions, Nonlinearity 35:6 (2022) 3159 | Journal | Preprint |

[65] M. Stadlbauer, P. Varandas and X. Zhang, Quenched and annealed equilibrium states for random Ruelle expanding maps and applications, Ergodic Theory and Dynamical Systems  43 (2023),  3150-3192  | Journal | Preprint | Slides |

[66]  M. Carvalho, V. Coelho, L. Salgado and P. Varandas, Sensitivity and historic behavior on Baire metric spaces, Ergodic Theory and Dynamical Systems (to appear) 44:1 (2024) 1-30 | Journal | Preprint | Slides |

[67] W. Bonomo, H. Lima and P. Varandas, Shape and stability of rotation sets for incompressible flows on the torus Td,, Israel Journal of Mathematics  (2024) https://doi.org/10.1007/s11856-024-2672-3 | Journal | Preprint |

[68] Y. Shi, X. Tian,  P. Varandas and X. Wang, On multifractal analysis and large deviations of singular-hyperbolic attractors, Nonlinearity  36:10 (2023) 5216| Journal | Preprint |

[69]  A. Biś, M Carvalho, M. Mendes, P. Varandas and X. Zhong, Correction:"Convex analysis approach to entropy functions, variational principles and equilibrium states", Communications in Mathematical Physics 401 (2023) 3335–3342  | Journal | Preprint | 

[70] J. F. Alves, W. Bahsoun, M. Ruziboev and P. Varandas, Quenched decay of correlations for nonuniformly hyperbolic random maps with an ergodic driving system, Nonlinearity 36 (2023) 3294 | Journal | Preprint | Slides |

[71] W. Bonomo,  J. Rocha and P. Varandas, Symmetries of C^r vector fields on surfaces, Bulletin of the Brazilian Mathematical Society (2023) 54:45 | Journal | Preprint |

[72] M. Carvalho, G. Pessil and P. Varandas, A convex analysis approach to metric mean dimension: limits of scaled pressures and variational principles, Advances in Mathematics 436 (2024) 109407 | Journal | Preprint | Slides

[73] T. Bomfim and P. Varandas, Phase transitions for surface diffeomorphisms, Bulletin of the Brazilian Mathematical Society  55 (2024) 28 | Journal | Preprint | 

[74] D. Daltro and P. Varandas, Exponential decay of correlations for Gibbs measures on attractors of Axiom A flows, Transactions of the American Mathematical Society (to appear)  | Journal | Preprint | Slides |

[75] I. Melbourne P. Varandas, Good inducing schemes for uniformly hyperbolic flows, and applications to exponential decay of correlations Annales Henri Poincaré (2024)  https://doi.org/10.1007/s00023-024-01439-w  | Journal | Preprint |

[76] W. Bonomo,  J. Rocha and P. Varandas, Symmetries of smooth flows and their time-t maps, Journal of Mathematical Analysis and Applications 539:2 (2024) 128534 | Journal | Preprint | 

[77] R. Bortolotti, E. Silva and P. Varandas, Regularity of the Hausdorff dimension of some hyperbolic systems, Journal of Mathematical Analysis and Applications  539 (2024) 128512 | Journal | Preprint | Slides |

[78]  M. Carvalho, F. Rodrigues and P. Varandas, Topological and metric emergence of continuous maps, Mathematical Proceedings of the Cambridge Philosophical Society 177:3 (2024) 525-551 | Journal | Preprint |

[79] A. Biś, M Carvalho, M. Mendes and P. Varandas, Variational principles and equilibrium states for group and semigroup actions, Studia Mathematica (to appear) | Preprint | Slides |

[80] A. Biś, M. Carvalho and P. Varandas, Variational principles for topological pressure of finitely generated pseudogroup actions, Groups, Geometry and Dynamics (to appear) | Preprint | Slides |

[81]  J. Siqueira, M. J. Torres and P. Varandas, Abundance of periodic orbits for typical impulsive flows, Journal of Differential Equations (to appear) | Preprint | Slides |

Proceedings of conferences & Book chapters

[1] N. Sumi, P. Varandas and K. Yamamoto, Specification and partial hyperbolicity for flows, Dynamical Systems, 30:4, (2015) 501-524. Proceedings of the ICM 2014, Satellite Conference on Dynamical Systems and Related Topics, Daejeon-Korea  | Journal | Preprint |

[2] S. Troubetzkoy and P. Varandas, On the role of continuity and expansiveness on LEO and periodic specification properties, CIRM Jean-Morlet Chair Subseries, Lecture Notes in Mathematics 2290, Springer-Verlag | Chapter | Preprint |

[3] P. Varandas, Some questions and remarks on Lyapunov irregular behavior for linear cocycles, Proceedings of the conference "New Trends on Lyapunov exponents", CIM Series in Mathematical Sciences, Springer-Verlag  eBook ISBN 978-3-031-41316-2| Book | Preprint | Slides |

Preprints

➣ M. Asaoka, Y. Nakano, P. Varandas and T. Yokoyama, Length averages for codimension one foliations | Preprint |

➣ V. Pinheiro and P. Varandas, Thermodynamic formalism for expanding measures | Preprint | Slides |

➣ M. Carvalho, U. Darji and P. Varandas, Shift operators and their classification  | Preprint | 

➣ R. Mohammadpour and P. Varandas, Multifractal formalism for Lyapunov exponents of fiber-bunched linear cocycles | Preprint |

➣ R. Mohammadpour and P. Varandas, Statistical properties of equilibrium states for fiber-bunched linear cocycles | Preprint |

➣  J. Siqueira, M. J. Torres and P. Varandas, On the periodic orbits of C0-typical impulsive semiflows | Preprint

➣ G. Ferreira and P. Varandas, Lyapunov ``non-typical" behavior for linear cocycles through  the lens of semigroup actions | Preprint | Slides |

PhD Thesis and Some Notes 

➣ I. Melbourne and  P. Varandas, Good inducing schemes for uniformly expanding maps

➣  B. Schapira and P. Varandas, A note on the space of Gibbs and Federer shift-invariant probability measures 

➣  P. Varandas, Topological methods in dynamics with applications in ergodic theory: old and new, CIM-Bulletin

➣  P. Varandas, A remark on the shadowing property for time-t maps of continuous flows 

➣  P. Varandas, PhD Thesis - IMPA  (slightly more general than the published results in [3])