Me

Publications

Book

Preprints

  1. R. Aimino, A.C.M. Freitas, J.M. Freitas, M. Todd, Multivariate extreme values for dynamical systems, Preprint version Sept 2024, arXiv:2406.14807.

  2. A.C.M. Freitas, J.M. Freitas, M. Todd, Enriched functional limit theorems for dynamical systems, Preprint version Jan 2024, arXiv:2011.10153.

Papers in peer reviewed journals

  1. A.C.M. Freitas, J.M. Freitas, I. Melbourne, M. Todd, Convergence to decorated Lévy processes in non-Skorohod topologies for dynamical systems, Electron. J. Probab., to appear.

  2. D. Bansard-Tresse, J.M. Freitas, Inducing techniques for quantitative recurrence and applications to Misiurewicz maps and doubly intermittent maps, Ann. Inst. Henri Poincaré Probab. Stat., to appear.

  3. C. Correia, A.C.M. Freitas, J.M. Freitas, Cluster distributions for dynamically defined point processes, Phys. D, 457, 133968, 2024.

  4. A.C.M. Freitas, J.M. Freitas, J.V. Soares, Rare events for product fractal sets, J. Phys. A: Math. Theor., 54, no. 34, 345202, 2021.

  5. A.C.M. Freitas, J.M. Freitas, M. Magalhães, S. Vaienti, Point processes of non stationary sequences generated by sequential and random dynamical systems, J. Stat. Phys., 181, no.4, 1365-1409, 2020.

  6. A.C.M. Freitas, J.M. Freitas, F.B. Rodrigues, J.V. Soares, Rare events for Cantor target sets, Comm. Math. Phys., 378, no. 1, 75-115, 2020.

  7. M. Abadi, A.C.M. Freitas, J.M. Freitas, Dynamical counterexamples regarding the Extremal Index and the mean of the limiting cluster size distribution, J. London Math. Soc., 102, no.2, 670-694, 2020.

  8. A.C.M. Freitas, J.M. Freitas, and M. Magalhães. Complete convergence and records for dynamically generated stochastic processes, Trans. Amer. Math. Soc., 373, no. 1, 435–478, 2020.

  9. R. Aimino, J.M. Freitas, Large deviations for dynamical systems with stretched exponential decay of correlations, Port. Math., 76, no. 2, 143-152, 2019.

  10. M. Abadi, A.C.M. Freitas, J.M. Freitas, Clustering indices and decay of correlations in non-Markovian models, Nonlinearity, 32, no. 12, 4853-4870, 2019.

  11. A.C.M. Freitas, J.M. Freitas, M. Magalhães, Convergence of Marked Point Processes of Excesses for Dynamical Systems, J. Eur. Math. Soc. (JEMS), 20, no. 9, 2131–2179, 2018.

  12. A.C.M. Freitas, J.M. Freitas, S. Vaienti, Extreme Value Laws for sequences of intermittent maps, Proc. Amer. Math. Soc., 146, no. 5, 2103–2116, 2018.

  13. A.C.M. Freitas, J.M. Freitas, S. Vaienti, Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems, Ann. Inst. Henri Poincaré Probab. Stat., 53, no. 3, 1341–1370, 2017.

  14. D. Azevedo, A.C.M. Freitas, J.M. Freitas, F.B. Rodrigues, Extreme Value Laws for dynamical systems with countable extremal sets, J. Stat. Phys., 167, no. 5, 1244–1261, 2017.

  15. A.C.M. Freitas, J.M. Freitas, M. Todd, S. Vaienti, Rare Events for the Manneville-Pomeau map, Stochastic Process. Appl., 126, no. 11, 3463–3479, 2016.

  16. M. Brito, A. C. M. Freitas, and J. M. Freitas. Tail prepivoting for the hill estimator, J. Phys. A: Math. Theor., 49, no. 19, 194004, 2016.

  17. D. Faranda, J. M. Freitas, P. Guiraud, and S. Vaienti. Statistical properties of random dynamical systems with contracting direction, J. Phys. A: Math. Theor., 49, no. 20, 204001, 2016.

  18. D. Faranda, J.M. Freitas, P. Guiraud, S. Vaienti, Extreme Value Theory for Piecewise Contracting Maps with Randomly Applied Stochastic Perturbations, Stoch. Dyn., 16, no. 3, 1660015, 23, 2016.

  19. D. Azevedo, A.C.M. Freitas, J.M. Freitas, F.B. Rodrigues, Clustering of extreme events created by multiple correlated maxima, Phys. D, 315, 33–48, 2016.

  20. M. Carvalho, A. C. M. Freitas, J. M. Freitas, M. Holland, and M. Nicol. Extremal dichotomy for uniformly hyperbolic systems. Dyn. Syst., 30, no. 4, 383–403, 2015.

  21. H. Aytac, J.M. Freitas, S. Vaienti, Laws of rare events for deterministic and random dynamical systems, Trans. Amer. Math. Soc., 367, no. 11, 8229–8278, 2015.

  22. D. Faranda, J.M. Freitas, P. Guiraud, S. Vaienti, Sampling local properties of attractors via Extreme Value Theory, Chaos Solitons Fractals, 74,55–66, 2015.

  23. A. C. M. Freitas, J. M. Freitas, and M. Todd. Speed of convergence for laws of rare events and escape rates, Stochastic Process. Appl., 125, no. 4, 1653–1687, 2015.

  24. J. M. Freitas, N. Haydn, and M. Nicol. Convergence of rare event point processes to the Poisson process for planar billiards, Nonlinearity, 27, no. 7, 1669–1687, 2014.

  25. D. Faranda, J.M. Freitas, V. Lucarini, G. Turcheti, S. Vaienti, Extreme value statistics for dynamical systems with noise, Nonlinearity, 26, no. 9, 2597–2622, 2013.

  26. J. M. Freitas. Extremal behaviour of chaotic dynamics, Dyn. Syst., 28, no. 3, 302–332, 2013.

  27. A.C.M. Freitas, J.M. Freitas, M. Todd, The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics, Comm. Math. Phys., 321, no. 2, 483-527, 2013.

  28. A.C.M. Freitas, J.M. Freitas, M. Todd, Extremal Index, Hitting Time Statistics and periodicity, Adv. Math., 231, no. 5, 2626-2665, 2012.

  29. J. F. Alves, J.M. Freitas, S. Luzzatto, S. Vaienti, From Rates of mixing to recurrence times via large deviations, Adv. Math., 228, no. 2, 1203–1236, 2011.

  30. A.C.M. Freitas, J.M. Freitas, M. Todd, Extreme Value Laws in Dynamical Systems for Non-smooth Observations, J. Stat. Phys., 142, no. 1, 108-126, 2011.

  31. J. M. Freitas, Exponential decay of hyperbolic times for benedicks-carleson quadratic maps, Port. Math., 67, no. 4, 525-540, 2010.

  32. J. F. Alves, M. Carvalho, J.M. Freitas, Statistical stability and continuity of SRB entropy for systems with Gibbs-Markov structures, Comm. Math. Phys., 296, no. 3, 739– 767, 2010.

  33. A.C.M. Freitas, J.M. Freitas, M. Todd, Hitting Time Statistics and Extreme Value Theory, Probab. Theory Related Fields, 147, no. 3, 675-710, 2010.

  34. J. F. Alves, M. Carvalho, J.M. Freitas, Statistical Stability for Hénon maps of the Benedicks-Carleson type, Ann. Inst. H. Poincaré Anal. Non Linéaire, 27, no. 2, 595-637, 2010.

  35. J.M. Freitas, M. Todd, Statistical stability of equilibrium states for interval maps, Nonlinearity, 22, no. 2, 259-281, 2009.

  36. A.C.M. Freitas, J.M. Freitas, Extreme Values for Benedicks-Carleson quadratic maps, Ergodic Theory Dynam. Systems, 28, no. 4, 1117-1133, 2008.

  37. A.C.M. Freitas, J.M. Freitas, On the link between dependence and independence in extreme value theory for dynamical systems, Stat. Probab. Lett., 78, no.9, 1088-1093, 2008.

  38. J.M. Freitas, Continuity of SRB measure and entropy for Benedicks-Carleson quadratic maps, Nonlinearity, 18, no.2, 831-854, 2005.
    (In 8., the argument is improved in order to obtain exponential estimates rather than subexponential and a problem with the combinatorics in the proof of Proposition 6.1 is corrected.)

Book chapters

  1. J.M. Freitas and M. Todd. Statistical stability for equilibrium states, in Dynamics, games and science. II, volume 2 of Springer Proc. Math., edited by M. Peixoto, A. Pinto, and D. Rand, pages 317–321. Springer, Heidelberg, 2011.

  2. A.C.M. Freitas, J.M. Freitas and M. Todd. Statistical properties of the maximum for non-uniformly hyperbolic dynamics, in Dynamics, games and science. I, volume 1 of Springer Proc. Math., edited by M. Peixoto, A. Pinto, and D. Rand, pages 365–374. Springer, Heidelberg, 2011.

  3. A.C.M. Freitas, J.M. Freitas, Quantificar o acaso, in “13 Viagens pelo Mundo da Matemática”, edited by C.Sá and J.Rocha, chapter 13, Universidade do Porto (2010).

Theses

The PhD thesis was awarded the Prize José Anastácio da Cunha by SPM (Portuguese Mathematical Society), distinguishing the best Portuguese PhD. Thesis in Mathematics during the period 2001-2006.