ترغب بنشر مسار تعليمي؟ اضغط هنا

Effective high-temperature estimates for intermittent maps

165   0   0.0 ( 0 )
 نشر من قبل Benoit Kloeckner
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English
 تأليف Beno^it Kloeckner




اسأل ChatGPT حول البحث

Using quantitative perturbation theory for linear operators, we prove spectral gap for transfer operators of various families of intermittent maps with almost constant potentials (high-temperature regime). Holder and bounded p-variation potentials are treated, in each case under a suitable assumption on the map, but the method should apply more generally. It is notably proved that for any Pommeau-Manneville map, any potential with Lispchitz constant less than 0.0014 has a transfer operator acting on Lip([0, 1]) with a spectral gap; and that for any 2-to-1 unimodal map, any potential with total variation less than 0.0069 has a transfer operator acting on BV([0, 1]) with a spectral gap. We also prove under quite general hypotheses that the classical definition of spectral gap coincides with the formally stronger one used in (Giulietti et al. 2015), allowing all results there to be applied under the high temperature bounds proved here: analyticity of pressure and equilibrium states, central limit theorem, etc.



قيم البحث

اقرأ أيضاً

We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in cite{FFV16}, where we g eneralised the theory of extreme values for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. The present work is an extension of our previous results for concatenations of uniformly expanding maps obtained in cite{FFV16}.
We construct Markov partitions for non-invertible and/or singular nonuniformly hyperbolic systems defined on higher dimensional Riemannian manifolds. The generality of the setup covers classical examples not treated so far, such as geodesic flows in closed manifolds, multidimensional billiard maps, and Viana maps, and includes all the recent results of the literature. We also provide a wealth of applications.
We revisit the relegation algorithm by Deprit et al. (Celest. Mech. Dyn. Astron. 79:157-182, 2001) in the light of the rigorous Nekhoroshevs like theory. This relatively recent algorithm is nowadays widely used for implementing closed form analytic p erturbation theories, as it generalises the classical Birkhoff normalisation algorithm. The algorithm, here briefly explained by means of Lie transformations, has been so far introduced and used in a formal way, i.e. without providing any rigorous convergence or asymptotic estimates. The overall aim of this paper is to find such quantitative estimates and to show how the results about stability over exponentially long times can be recovered in a simple and effective way, at least in the non-resonant case.
70 - Diana A. Mendes 2003
The main purpose of this paper is to present a kneading theory for two-dimensional triangular maps. This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map. We also d efine a Markov partition by rectangles for the phase space of these maps. A direct consequence of these results is the rigorous computation of the topological entropy of two-dimensional triangular maps. The connection between kneading theory and subshifts of finite type is shown by using a commutative diagram derived from the homological configurations associated to $m-$modal maps of the interval.
458 - Caroline L. Wormell 2021
Intermittent maps of the interval are simple and widely-studied models for chaos with slow mixing rates, but have been notoriously resistant to numerical study. In this paper we present an effective framework to compute many ergodic properties of the se systems, in particular invariant measures and mean return times. The framework combines three ingredients that each harness the smooth structure of these systems induced maps: Abel functions to compute the action of the induced maps, Euler-Maclaurin summation to compute the pointwise action of their transfer operators, and Chebyshev Galerkin discretisations to compute the spectral data of the transfer operators. The combination of these techniques allows one to obtain exponential convergence of estimates for polynomially growing computational outlay, independent of the order of the maps neutral fixed point. This enables numerical exploration of intermittent dynamics in all parameter regimes, including in the infinite ergodic regime.
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