ترغب بنشر مسار تعليمي؟ اضغط هنا

SRB measures for Anosov actions

88   0   0.0 ( 0 )
 نشر من قبل Colin Guillarmou
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Given a general Anosov abelian action on a closed manifold, we study properties of certain invariant measures that have recently been introduced in cite{BGHW20} using the theory of Ruelle-Taylor resonances. We show that these measures share many properties of Sinai-Ruelle-Bowen measures for general Anosov flows such as smooth desintegrations along the unstable foliation, positive Lebesgue measure basins of attraction and a Bowen formula in terms of periodic orbits.



قيم البحث

اقرأ أيضاً

We define for $mathbb{R}^kappa$-Anosov actions a notion of joint Ruelle resonance spectrum by using the techniques of anisotropic Sobolev spaces in the cohomological setting of joint Taylor spectra. We prove that these Ruelle-Taylor resonances are in trinsic and form a discrete subset of $mathbb{C}^kappa$ and that $0$ is always a leading resonance. The joint resonant states at $0$ give rise to measures of SRB type and the mixing properties of these measures are related to the existence of purely imaginary resonances. The spectral theory developed in this article applies in particular to the case of Weyl chamber flows and provides a new way to study such flows.
200 - Zeng Lian , Peidong Liu , 2016
In this paper, we study the existence of SRB measures for infinite dimensional dynamical systems in a Banach space. We show that if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has an SRB measure.
115 - Luchezar Stoyanov 2013
We prove exponential decay of correlations for Holder continuous observables with respect to any Gibbs measure for contact Anosov flows admitting Pesin sets with exponentially small tails. This is achieved by establishing strong spectral estimates fo r certain Ruelle transfer operators for such flows.
156 - Shilei Fan , Yanqi Qiu 2017
In this note, we give a nature action of the modular group on the ends of the infinite (p + 1)-cayley tree, for each prime p. We show that there is a unique invariant probability measure for each p.
For compact and for convex co-compact oriented hyperbolic surfaces, we prove an explicit correspondence between classical Ruelle resonant states and quantum resonant states, except at negative integers where the correspondence involves holomorphic sections of line bundles.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا