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math.DS2021
Topological weak mixing and diffusion at all times for a class of Hamiltonian systems
Bassam Fayad, Maria Saprykina
We present examples of nearly integrable analytic Hamiltonian systems with several strong diffusion properties: topological weak mixing and diffusion at all times. These examples a…
math.DS2021
Realizing arbitrary -dimensional dynamics by renormalization of -perturbations of identity
Bassam Fayad, Maria Saprykina
Any conservative map of the -dimensional unit ball can be realized by renormalized iteration of a perturbation of identity: there exists a conserva…
math.DS2021
Multiple Borel Cantelli Lemma in dynamics and MultiLog law for recurrence
Dmitry Dolgopyat, Bassam Fayad, Sixu Liu
A classical Borel Cantelli Lemma gives conditions for deciding whether an infinite number of rare events will almost surely happen. In this article, we propose an extension of Bore…