Publications
Davor Dragicevic, Cesar M. Silva & Helder Vilarinho, Admissibility and generalized nonuniform dichotomies for nonautonomous Random Dynamical Systems. https://arxiv.org/abs/2410.13697
Bento, A. J. G. & Vilarinho, H. Center manifolds for Random Dynamical Systems with generalized trichotomies. https://arxiv.org/abs/2408.01204. [pdf]
Bessa, M. & Vilarinho, H. On the stability of x¨(t)+α(t)x˙(t)+β(t)x(t)=0. arxiv.org/abs/2404.02066 [pdf]
Asad Ullah & Helder Vilarinho. Decay of Correlations via induced Weak Gibbs Markov maps for non-Hölder observables. arxiv.org/abs/2403.09528 [pdf]
Asad Ullah & Helder Vilarinho. Statistical properties of dynamical systems via induced weak Gibbs Markov maps. arXiv:2311.17531 [pdf]
Amaro, D., Bessa, M. & Vilarinho, H. (2024). Simple Lyapunov spectrum for linear homogeneous differential equations with L^p parameters. Nonlinear Differ. Equ. Appl. 31, 43. https://doi.org/10.1007/s00030-024-00931-w
Amaro, D., Bessa, M. & Vilarinho, H. (2024) Genericity of trivial Lyapunov spectrum for Lp-cocycles derived from second order linear homogeneous differential equations. Journal of Differential Equations, Volume 380, 228-253. https://doi.org/10.1016/j.jde.2023.10.033
Jesus, L. F., Silva, C. M. & Vilarinho, H. (2022). An eco-epidemiological model with general functional response of predator to prey. Mathematical Methods in the Applied Sciences. https://doi.org/10.1002/mma.8743
Jesus, L. F., Silva, C. M. & Vilarinho, H. (2022). Random perturbations of an eco-epidemiological model. Discrete & Continuous Dynamical Systems – B 27 (1) : 257-275. doi: 10.3934/dcdsb.2021040
Alves, J. F., Dias, C. L. & Vilarinho, H. (2021) On the liftability of expanding stationary measures. Stochastic and Dynamics. Vol. 21, No. 06, 2150039 (2021) https://doi.org/10.1142/S0219493721500398
Jesus, L. F., Silva, C. M. & Vilarinho, H. (2021). Dynamics of a discrete eco-epidemiological model with disease in the prey. Journal of Difference Equations and Applications 27 (1), 132-155. https://doi.org/10.1080/10236198.2021.1876682
Bento, A. J. G. & Vilarinho, H. (2021). Invariant manifolds for Random Dynamical Systems on Banach Spaces exhibiting generalized dichotomies. Journal of Dynamics and Differential Equations 33, 111–133. https://doi.org/10.1007/s10884-020-09888-7.
Jesus, L. F., Silva, C. M. & Vilarinho, H. (2020). Periodic orbits for periodic eco-epidemiological systems with infected prey, Electron. J. Qual. Theory Differ. Equ., 54, 1-20. https://doi.org/10.14232/ejqtde.2020.1.54
Bessa, M., Silva, C. M. & Vilarinho, H. (2018). Stretching generic Pesins’ formula. Journal of Statistical Physics. https://doi.org/10.1007/s10955-018-2163-1
Li, X. & Vilarinho, H. (2018). Almost sure mixing rates for non-uniformly expanding maps. Stochastics and Dynamics, 18 (3). https://doi.org/10.1142/S0219493718500272
Bessa, M. & Vilarinho, H. (2014.) Fine properties of $L^p$-cocycles which allow abundance of simple and trivial spectrum. Journal of Differential Equations, 256 (7), 233-2367. http://dx.doi.org/10.1016/j.jde.2014.01.003
Pacheco, R. & Vilarinho, H. (2013). Metrics on tiling spaces, local isomorphism and an application of brown’s lemma. Monatshefte Fur Mathematik, 170 (2), 205-225. http://dx.doi.org/10.1007/s00605-013-0484-3
Pacheco, R. & Vilarinho, H. (2013). Statistical stability for multi-substitution tiling spaces. Discrete and Continuous Dynamical Systems- Series A, 33 (10), 4579-4594. https://doi.org/10.1017/S0143385712000077
Alves, J. F. & Vilarinho, H. (2013). Strong stochastic stability for non-uniformly expanding maps. Ergodic Theory and Dynamical Systems, 33 (3), 647-692. https://doi.org/10.1017/S0143385712000077
Theses
Torres Markovianas, decaimento de correlações e transformações expansoras, Master thesis (Portuguese), 2003.
Strong stochastic stability for non-uniformly expanding maps, Ph. D. thesis, 2010.