9 citations · 20 across the 11 of their papers we have counts for
11 papers
Intermingled basins: Kan's example on the Riemann sphere
Abbas Fakhari, Ale Jan Homburg, Sebastian van Strien
Kan's discovery of dynamical systems with two attractors whose basins of attraction both have full support, featured specific examples of skew product systems of interval diffeomor…
Generalized Horseshoe Maps part I: limit laws and absolute continuity of physical measure
Abbas Fakhari, Maisam Hedyehloo, Mohammad Soufi
We apply thermodynamic formalism to a generalized horseshoe map. We prove that a tailored anisotropic Banach space with weighted norms yields a spectral gap for the transfer operat…
Thick attractors with intermingled basins
Abbas Fakhari, Ale Jan Homburg
We construct various novel and elementary examples of dynamics with metric attractors that have intermingled basins. A main ingredient is the introduction of random walks along orb…
Stable local dynamics: expansion, quasi-conformality and ergodicity
Abbas Fakhari, Meysam Nassiri, Hesam Rajabzadeh
In this paper, we study stable ergodicity of the action of groups of diffeomorphisms on smooth manifolds. Such actions are known to exist only on one-dimensional manifolds. The aim…
Absolutely Continuous Invariant Measure for Generalized Horseshoe Maps
Abbas Fakhari, Maryam Khalaj
In this paper, we study the SRB measures of generalized horseshoe map. We prove that under the conditions of transversality and fatness, the SRB measure is actually absolutely cont…
Ergodicity of non-autonomous discrete systems with non-uniform expansion
Pablo G. Barrientos, Abbas Fakhari
We study the ergodicity of non-autonomous discrete dynamical systems with non-uniform expansion. As an application we get that any uniformly expanding finitely generated semigroup…
SRB measures for certain class of non-uniformly hyperbolic endomorphisms on the solid torus
A. Ehsani, A. Fakhari, F. H. Ghane +1
In this paper we address the existence and ergodicity of non-hyperbolic attracting sets for a certain class of smooth endomorphisms on the solid torus. Such systems allow a formula…
Saturation of Generalized Partially Hyperbolic Attractors
A. Fakhari, M. Soufi
We prove the saturation of a generalized partially hyperbolic attractor of a map. As a consequence, we show that any generalized partially hyperbolic horseshoe-like attractor…
Expanding actions: minimality and ergodicity
Pablo G. Barrientos, Abbas Fakhari, Dominique Malicet +1
We prove that every expanding minimal semigroup action of diffeomorphisms of a compact manifold (resp. conformal) is robustly minimal (resp. ergodic with respect to…
Connectedness of the set of central Lyapunov exponents
Abbas Fakhari
We show that there is a residual subset of such that for any and any partially hyperbolic homoclinic class with one dimensional…
Density of fiberwise orbits in minimal iterated function systems on the circle
Pablo G. Barrientos, Abbas Fakhari, Ali Sarizadeh
We study the minimality of almost every orbital branch of minimal iterated function systems (IFSs). We prove that this kind of minimality holds for forward and backward minimal IFS…