ترغب بنشر مسار تعليمي؟ اضغط هنا

Symbolic dynamics and transfer operators for Weyl chamber flows: a class of examples

51   0   0.0 ( 0 )
 نشر من قبل Anke Pohl
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English
 تأليف Anke Pohl




اسأل ChatGPT حول البحث

We provide special cross sections for the Weyl chamber flow on a sample class of Riemannian locally symmetric spaces of higher rank, namely the direct product spaces of Schottky surfaces. We further present multi-parameter transfer operator families for the discrete dynamical systems on Furstenberg boundary that are related to these cross sections.



قيم البحث

اقرأ أيضاً

274 - Luchezar Stoyanov 2010
For Axiom A flows on basic sets satisfying certain additional conditions we prove strong spectral estimates for Ruelle transfer operators similar to these of Dolgopyat (1998) for geodesic flows on compact surfaces (for general potentials)and transiti ve Anosov flows on compact manifolds with C^1 jointly non-integrable horocycle foliations (for the Sinai-Bowen-Ruelle potential). Here we deal with general potentials. As is now well known, such results have deep implications in some related areas, e.g. in studying analytic properties of Ruelle zeta functions and partial differential operators, closed orbit counting functions, decay of correlations for Holder continuous potentials.
122 - 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.
220 - Yuri Lima , Omri Sarig 2014
We construct symbolic dynamics on sets of full measure (w.r.t. an ergodic measure of positive entropy) for $C^{1+epsilon}$ flows on compact smooth three-dimensional manifolds. One consequence is that the geodesic flow on the unit tangent bundle of a compact $C^infty$ surface has at least const $times(e^{hT}/T)$ simple closed orbits of period less than $T$, whenever the topological entropy $h$ is positive -- and without further assumptions on the curvature.
We study rank-two symbolic systems (as topological dynamical systems) and prove that the Thue-Morse sequence and quadratic Sturmian sequences are rank-two and define rank-two symbolic systems.
125 - David Burguet , Ruxi Shi 2021
A zero-dimensional (resp. symbolic) flow is a suspension flow over a zero-dimensional system (resp. a subshift). We show that any topological flow admits a principal extension by a zero-dimensional flow. Following [Bur19] we deduce that any topologic al flow admits an extension by a symbolic flow if and only if its time-$t$ map admits an extension by a subshift for any $t eq 0$. Moreover the existence of such an extension is preserved under orbit equivalence for regular topological flows, but this property does not hold more true for singular flows. Finally we investigate symbolic extensions for singular suspension flows. In particular, the suspension flow over the full shift on ${0,1}^{mathbb Z}$ with a roof function $f$ vanishing at the zero sequence $0^infty$ admits a principal symbolic extension or not depending on the smoothness of $f$ at $0^infty$.
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