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Search Results: 1 - 10 of 18491 matches for " Ali Tahzibi "
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Stably ergodic diffeomorphisms which are not partially hyperbolic
Ali Tahzibi
Mathematics , 2002,
Abstract: We show stable ergodicity of a class of conservative diffeomorphisms which do not have any hyperbolic invariant subbundle. Moreover the uniqueness of SRB measures for non-conservative $C^1$ perturbations of such diffeomorphisms. This class contains strictly non-partially hyperbolic robustly transitive diffeomorphisms by Bonatti-Viana and so we answer their question about the stable ergodicity of such systems.
Robust transitivity implies almost robust ergodicity
Ali Tahzibi
Mathematics , 2002,
Abstract: In this paper we show the relation between robust transitivity and robust ergodicity for conservative diffeomorphisms. In dimension 2 robustly transitive systems are robustly ergodic. For the three dimensional case, we define it almost robust ergodicity and prove that generically robustly transitive systems are almost robustly ergodic, if the Lyapunov exponents are nonzero. We also show in higher dimensions, that under some conditions robust transitivity implies robust ergodicity.
A lower bound for topological entropy of generic non Anosov symplectic diffeomorphisms
Thiago Catalan,Ali Tahzibi
Mathematics , 2010, DOI: 10.1017/etds.2013.12
Abstract: We prove that a $C^1-$generic symplectic diffeomorphism is either Anosov or the topological entropy is bounded from below by the supremum over the smallest positive Lyapunov exponent of the periodic points. We also prove that $C^1-$generic symplectic diffeomorphisms outside the Anosov ones do not admit symbolic extension and finally we give examples of volume preserving diffeomorphisms which are not point of upper semicontinuity of entropy function in $C^1-$topology.
Homoclinic tangency and variation of entropy
Marcus Bronzi,Ali Tahzibi
Mathematics , 2010,
Abstract: In this paper we study the effect of a homoclinic tangency in the variation of the topological entropy. We prove that a diffeomorphism with a homoclinic tangency associated to a basic hyperbolic set with maximal entropy is a point of entropy variation in the $C^{\infty}$-topology. We also prove results about variation of entropy in other topologies and when the tangency does not correspond to a basic set with maximal entropy. We also show an example of discontinuity of the entropy among $C^{\infty}$ diffeomorphisms of three dimensional manifolds.
Robustly transitive actions of $R^2$ on compact three manifolds
Ali Tahzibi,Carlos Maquera
Mathematics , 2006,
Abstract: In this paper, we define $C^1$-robust transitivity for actions of $\RR^2$ on closed connected orientable manifolds. We prove that if the ambient manifold is three dimensional and the dense orbit of a robustly transitive action is not planar, then it is "degenerate" and the action is defined by an Anosov flow.
SRB measures and homoclinic relation for Endomorphisms
Pouya Mehdipour,Ali Tahzibi
Mathematics , 2015,
Abstract: In this paper we give an upper bound for the number of SRB measures of saddle type of local diffeomorphisms of boundaryless manifolds in terms of maximal cardinality of set of periodic points without any homoclinic relation.
Regularity of foliations and Lyapunov exponents of partially hyperbolic dynamics
Fernando Micena,Ali Tahzibi
Mathematics , 2012, DOI: 10.1088/0951-7715/26/4/1071
Abstract: In this work we study relations between regularity of invariant foliations and Lyapunov exponents of partially hyperbolic diffeomorphisms. We suggest a new regularity condition for foliations in terms of desintegration of Lebesgue measure which can be considered as a criterium for rigidity of Lyapunov exponents.
Central Lyapunov exponent of partially hyperbolic diffeomorphisms of $\mathbb{T}^3$
Gabriel Ponce,Ali Tahzibi
Mathematics , 2012,
Abstract: In this paper we construct some "pathological" volume preserving partially hyperbolic diffeomorphisms on $\toro{3}$ such that their behaviour in small scales in the central direction (Lyapunov exponent) is opposite to the behavior of their linearization. These examples are isotopic to Anosov. We also get partially hyperbolic diffeomorphisms isotopic to Anosov (consequently with non-compact central leaves) with zero central Lyapunov exponent at almost every point.
Center Lyapunov exponents in partially hyperbolic dynamics
Andrey Gogolev,Ali Tahzibi
Mathematics , 2013,
Abstract: We survey a collection of recent results on center Lyapunov exponents of partially hyperbolic diffeomorphisms. We explain several ideas in simplified setups and formulate the general versions of results. We also pose some open questions.
Stochastic stability at the boundary of expanding maps
Vitor Araujo,Ali Tahzibi
Mathematics , 2004, DOI: 10.1088/0951-7715/18/3/001
Abstract: We consider endomorphisms of a compact manifold which are expanding except for a finite number of points and prove the existence and uniqueness of a physical measure and its stochastical stability. We also characterize the zero-noise limit measures for a model of the intermittent map and obtain stochastic stability for some values of the parameter. The physical measures are obtained as zero-noise limits which are shown to satisfy Pesin?s Entropy Formula.
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