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9 papers · 2 filters
Shades of Hyperbolicity for Hamiltonians
M. Bessa, J. Rocha, M. J. Torres
We prove that a C2 Hamiltonian system H in M is globally hyperbolic if any of the following statements holds: H is robustly topologically stable; H is stably shadowable; H is stabl…
Statistical stability of Geometric Lorenz attractors
Jose F. Alves, Mohammad Soufi
We consider the robust family of Geometric Lorenz attractors. These attractors are chaotic in the sense that they are transitive and have sensitive dependence on the initial condit…
Extreme value statistics for dynamical systems with noise
Davide Faranda, Jorge Milhazes Freitas, Valerio Lucarini +2
We study the distribution of maxima (Extreme Value Statistics) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic…
Laws of rare events for deterministic and random dynamical systems
Hale Aytaç, Jorge Milhazes Freitas, Sandro Vaienti
The object of this paper is twofold. From one side we study the dichotomy, in terms of the Extremal Index of the possible Extreme Value Laws, when the rare events are centred aroun…
Periodic points of Ruelle-expanding maps
Maria Carvalho, Mário Alexandre Magalhães
We prove that, for a Ruelle-expanding map, the zeta function is rational and the topological entropy is equal to the exponential growth rate of the periodic points.
Statistical stability and limit laws for Rovella maps
Jose F. Alves, Mohammad Soufi
We consider the family of one-dimensional maps arising from the contracting Lorenz attractors studied by Rovella. Benedicks-Carleson techniques were used by Rovella to prove that t…