Kam theorem for gevrey hamiltonians
Web7 dec. 2024 · KAM theorem for Gevrey Hamiltonians G. Popov Mathematics Ergodic Theory and Dynamical Systems 2004 We consider Gevrey perturbations H of a completely … Web9 apr. 2016 · If the Hamiltonian is real-analytic, the tori are real analytic. This follows at once from a Birkhoff normal form and a classical version of the KAM theorem. Now if ω is Liouville (which means not Diophantine), the Birkhoff normal form no longer makes sense.
Kam theorem for gevrey hamiltonians
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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 ... WebKAM HAMILTONIANS ARE NOT QUANTUM ERGODIC SEAN GOMES´ Abstract. We show that under generic conditions, the quantisation of a 1-parameter family of KAM perturbations P(x,ξ;t) of a completely integrable and Kolmogorov non-degenerate Gevrey smooth Hamiltonian is not quantum ergodic, at least for a full measure subset of the parameter t …
WebarXiv: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 … WebAbstract. We consider Gevrey perturbations $H$ of a completely integrable Gevrey Hamiltonian $H_0$. Given a Cantor set $\Omega_\kappa$ defined by a Diophantine ...
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. … WebKAM Hamiltonians are not Quantum Ergodic S. Gomes Mathematics, Physics 2024 We show that under generic conditions, the quantisation of a $1$-parameter family of KAM …
Web19 mai 2024 · We prove a new invariant torus theorem, for -Gevrey smooth Hamiltonian systems, under an arithmetic assumption which we call the -Bruno-Rüssmann condition, and which reduces to the classical Bruno-Rüssmann condition in the analytic category.
Web31 mar. 2009 · Abstract A Gevrey symplectic normal form of an analytic and more generally Gevrey smooth Hamiltonian near a Lagrangian invariant torus with a Diophantine vector of rotation is obtained. The normal form implies effective stability of the quasi-periodic motion near the torus. Keywords: Birkhoff normal form, Kronecker tori, effective stability, indigenous ethics definitionWeb19 mai 2024 · – We prove a theorem about the stability of action variables for Gevrey quasi-convex near-integrable Hamiltonian systems and construct in that context a system with … locksmith pontefractWeb19 mai 2024 · We prove a new invariant torus theorem, for $α$-Gevrey smooth Hamiltonian systems , under an arithmetic assumption which we call the $α$-Bruno-R{ü}ssmann condition , and which reduces to the classical Bruno-R{ü}ssmann condition in the analytic category. Our proof is direct in the sense that, for analytic Hamiltonians, we avoid the use … indigenous essay topicsWeb19 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 … locksmith pomona caWeb19 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 … indigenous ethnicityWebThe two main stability results for nearly integrable Hamiltonian systems are revisited: Nekhoroshev theorem, concerning exponential lower bounds for the stability time (effective stability), and KAM theorem, concerning the preservation of a majority of the nonresonant invariant tori (perpetual stability). To stress the relationship between both theorems, a … locksmith port angeles waWebWe 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. locksmith port hawkesbury