Intrinsic ergodicity of partially hyperbolic diffeomorphisms with a hyperbolic linear part

Ures, Raúl

doi:10.1090/s0002-9939-2011-11040-2

Cited by 81 publications

(87 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Section 6 explores some more or less direct consequences of our result. First, we study the existence and finiteness of maximal entropy measures which are a direct application of our main results and previous ones [29,32]. Then, we obtain another dynamical consequence which holds for partially hyperbolic diffeomorphisms of non-toral nilmanifolds: Proposition 1.9.…”

Section: Introductionmentioning

confidence: 69%

“…In this subsection, we observe how our results allow one to re-obtain some results about entropy maximizing measures previously proved under less generality. First, the main result of [32] also holds in the pointwise case. Proposition 6.1.…”

Section: Entropy Maximizing Measuresmentioning

confidence: 96%

“…Proof. The only dependence on absolute partial hyperbolicity in [32] is in establishing Lemmas 3.2 and 3.3. Those lemmas can be proved directly from Corollary 1.5 of this paper.…”

Section: Entropy Maximizing Measuresmentioning

confidence: 99%

See 2 more Smart Citations

Pointwise partial hyperbolicity in three-dimensional nilmanifolds

Hammerlindl¹,

Potrie²

2014

Journal of the London Mathematical Society

View full text Add to dashboard Cite

Abstract. We show the existence of a family of manifolds on which all (pointwise or absolutely) partially hyperbolic systems are dynamically coherent. This family is the set of 3-manifolds with nilpotent, non-abelian fundamental group. We further classify the partially hyperbolic systems on these manifolds up to leaf conjugacy. We also classify those systems on the 3-torus which do not have an attracting or repelling periodic 2-torus. These classification results allow us to prove some dynamical consequences, including existence and uniqueness results for measures of maximal entropy and quasiattractors.

show abstract

Section: Introductionmentioning

confidence: 69%

Section: Entropy Maximizing Measuresmentioning

confidence: 96%

See 1 more Smart Citation

Pointwise partial hyperbolicity in three-dimensional nilmanifolds

Hammerlindl¹,

Potrie²

2014

Journal of the London Mathematical Society

View full text Add to dashboard Cite

show abstract

“…By Franks [22], for any f ∈ A(L), there is a unique semi-conjugacy h f between f and L which is isotopic to the identity map. We need the following standard topological classification of derived from Anosov diffeomorphism by [9,29,30,66,76]: In particular, if f is an Anosov diffeomorphism, by Franks [22], the semi-conjugacy h f is indeed a conjugacy. Denote by F s f , F wu f , F su f the stable, weak-unstable and strong unstable foliation of f .…”

Section: Three Dimensional Anosov (Proof Of Theorem A)mentioning

confidence: 99%

Lyapunov exponents and rigidity of Anosov automorphisms and skew products

Saghin

Yang

2019

Advances in Mathematics

View full text Add to dashboard Cite

In this paper we obtain local rigidity results for linear Anosov diffeomorphisms in terms of Lyapunov exponents. More specifically, we show that given an irreducible linear hyperbolic automorphism L with simple real eigenvalues with distinct absolute values, any small perturbation preserving the volume and with the same Lyapunov exponents is smoothly conjugate to L.We also obtain rigidity results for skew products over Anosov diffeomorphisms. Given a volume preserving partially hyperbolic skew product diffeomorphism f 0 over an Anosov automorphism of the 2-torus, we show that for any volume preserving perturbation f of f 0 with the same average stable and unstable Lyapunov exponents, the center foliation is smooth.

show abstract

“…[16] The semi-conjugacy is uniformly close to the identity [4, Proposition 2.3.1], let us say by a constant C, that is ||H (x) − x|| < C, ∀x ∈ R 3 .…”

Section: Lemma 33mentioning

confidence: 99%

Lyapunov exponents and smooth invariant foliations for partially hyperbolic diffeomorphisms on

Varão¹

2015

Dynamical Systems

View full text Add to dashboard Cite

This paper is concerned with the rigidity problem for volume preserving partially hyperbolic diffeomorphisms on T 3 homotopic to a linear Anosov on T 3 . We characterize the C 1 + θ conjugacy of such diffeomorphisms in terms of smooth conditions on the stable and unstable foliations. The smooth conditions on the foliations are to be C 1 foliations and transversely absolutely continuous with bounded Jacobians. In particular these conditions for only one direction (stable, centre or unstable) completely determine the Lyapunov exponents.

show abstract

Intrinsic ergodicity of partially hyperbolic diffeomorphisms with a hyperbolic linear part

Abstract: Abstract. We prove that any (absolutely) partially hyperbolic diffeomorphism f of T 3 homotopic to a hyperbolic automorphism A is intrinsically ergodic; that is, it has a unique entropy maximizing measure μ.

Cited by 81 publications

References 18 publications

Pointwise partial hyperbolicity in three-dimensional nilmanifolds

Pointwise partial hyperbolicity in three-dimensional nilmanifolds

Lyapunov exponents and rigidity of Anosov automorphisms and skew products

Lyapunov exponents and smooth invariant foliations for partially hyperbolic diffeomorphisms on

Contact Info

Product

Resources

About