Kam theorem for gevrey hamiltonians
Web1 dec. 2010 · A major result about perturbations of integrable Hamiltonian systems is the Nekhoroshev theorem, which gives exponential stability for all solutions provided the system is analytic and the... Web9 nov. 2024 · In the proof of our theorem, we use a modified KAM iteration with some parameters as in [26, 28–30], which is proposed by Pöschel . The aim of KAM iteration is to eliminate the lower order terms of \(y\) in small perturbation \(f^{1}\) and \(f^{2}\) , which yields that we obtain a Gevrey normal form ( 5 ) of area preserving mappings, which ...
Kam theorem for gevrey hamiltonians
Did you know?
Web15 oct. 2016 · Popov G.: KAM theorem for Gevrey Hamiltonians. Ergod. Theory Dyn. Syst. 24 (5), 1753–1786 (2004) MathSciNet Article MATH Google Scholar Pöschel, J.: A lecture on the classical KAM theory. In: Katok, A. et al., (eds.) Smooth Ergodic Theory and its Applications (Seattle, WA, 1999), Proc. Symp. Pure Math., vol. 69, pp. 707–732. WebErgod. Th. & Dynam. Sys.(2004),24, 1753–1786 c 2004 Cambridge University Press DOI: 10.1017/S0143385704000458 Printed in the United Kingdom KAM theorem for Gevrey Hamiltonians G
WebErgod. Th. & Dynam. Sys.(2004),24, 1753–1786 c 2004 Cambridge University Press DOI: 10.1017/S0143385704000458 Printed in the United Kingdom KAM theorem for Gevrey … Web2 iun. 2013 · It enables us to deal with non-analytic Hamiltonians, and in this first part we will focus on Gevrey Hamiltonians and derive normal forms with an exponentially small remainder. This extends a result which was known for analytic Hamiltonians, and only in the periodic case for Gevrey Hamiltonians. ... A Diophantine Duality Applied to the KAM and ...
Web3 mai 2024 · A Nekhoroshev type theorem for the nonlinear wave equation, Pure and Applied Mathematics Quarterly, preprint. Popov, G., KAM theorem for Gevrey Hamiltonians, Ergodic Theory Dynam. Systems, 24, 2004, 1753–1786. … Websummation allow to find a Gevrey (convergent) normal form with an exponentially small remainder, and this is all what is needed to prove the Nekhoroshev theorem for quasi-convex Hamiltonians. Examples of Arnold diffusion were also obtained in [MS02] but in the Gevrey non-analytic case α>1, as the method uses the existence of bump functions.
Web1 KAM theorem for Gevrey Hamiltonians Let D0 be a bounded domain in Rn, and Tn = Rn/2πZn, n ≥ 2. We consider a class of real valued Gevrey Hamiltonians in Tn × D0 which …
WebWe prove a new invariant torus theorem, for α-Gevrey smooth Hamiltonian sys-tems, under an arithmetic assumption which we call the α-Bruno-Ru¨ssmann condi-tion, and which reduces to the classical Bruno-Ru¨ssmann condition in the analytic category. Our proof is direct in the sense that, for analytic Hamiltonians, we avoid lyons health departmentWebKAM theory: the effect of small denominators in Fourier series reduces to decreasing the “Gevrey width” s, the analogue of the analyticity width. This makes it possible to adapt … lyons health clinic houston txWebarXiv:math/0305264v1 [math.DS] 19 May 2003 KAM Theorem for Gevrey Hamiltonians G. Popov Abstract We consider Gevrey perturbations H of a completely integrable Gevrey … lyons health center nyWebWe obtain also a quantum Birkho normal form for the corresponding class of h-pseudodierential operators with Gevrey symbols and construct quasimodes with exponen-tially small error terms. 1 KAM theorem for Gevrey Hamiltonians Let D0 be a bounded domain in Rn, and Tn = Rn=2Zn, n 2. lyons health clinic houstonWeb19 mai 2003 · Title:KAM Theorem for Gevrey Hamiltonians. Authors:Georgi Popov. Download PDF. Abstract:We consider Gevrey perturbations $H$ of a completely integrable GevreyHamiltonian $H_0$. Given a Cantor set $\Omega_\kappa$ defined by a … kiptopeke state park lodge picturesWeb19 mai 2003 · KAM Hamiltonians are not Quantum Ergodic S. Gomes Mathematics, Physics 2024 We show that under generic conditions, the quantisation of a $1$-parameter family … lyons heating and cooling winfield wvWebbility in the Nekhoroshev Theorem for the quasi-convex case, to the situation in which the Hamiltonian function is only assumed to belong to some Gevrey class instead of being real-analytic. For n degrees of freedom and Gevrey-α Hamiltonians, α ≥ 1, we prove that one can choose a = 1/2nα as an exponent for the time of stability and b = 1/2n lyons heating and cooling scholfield wi