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137 papers · 1 filter
A functional limit theorem for a dynamical system with an observable maximised on a Cantor set
Raquel Couto, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas +1
We consider heavy-tailed observables maximised on a dynamically defined Cantor set and prove convergence of the associated point processes as well as functional limit theorems. The…
Robust heteroclinic cycles in pluridimensions
Sofia B. S. D. Castro, Alastair M. Rucklidge
Heteroclinic cycles are sequences of equilibria along with trajectories that connect them in a cyclic manner. We investigate a class of robust heteroclinic cycles that does not sat…
Bifurcations and canards in the FitzHugh-Nagumo system: a tutorial in fast-slow dynamics
Bruno F. F. Gonçalves, Isabel S. Labouriau, Alexandre A. P. Rodrigues
In this article, we study the FitzHugh-Nagumo --fast-slow system where the vector fields associated to the slow/fast equations come from the reduction of the Hodgin-Huxley m…
Metric mean dimension via subshifts of compact type
Gustavo Pessil
We investigate the metric mean dimension of subshifts of compact type. We prove that the metric mean dimensions of a continuous map and its inverse limit coincide, generalizing Bow…
Compound Poisson distributions for random dynamical systems using probabilistic approximations
Lucas Amorim, Nicolai Haydn, Sandro Vaienti
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly…
Complex ODEs, singularity theory and dynamics
Helena Reis
These notes are a slightly enlarged version of my habilitation thesis, where our research interest and main results in the past few years are summarized. Most of the discussion rev…