COMPUTER-ASSISTED PROOFS OF EXISTENCE OF QUASI-PERIODIC SYSTEMS VIA FOURIER METHODS

被引：0

作者：

Haro, Alex ^{[1
,2
]}

Vidal, Eric sandin ^{[3
]}

机构：

[1] Univ Barcelona, Dept Matemat & Informat, Gran Via 585, Barcelona 08007, Spain

[2] Ctr Recerca Matemat, Edifici C,Campus Bellaterra, Bellaterra 08193, Spain

[3] Vrije Univ Amsterdam, Fac Sci, Dept Math, Boelelaan 1111, NL-1081 HV Amsterdam, Netherlands

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2024年

关键词：

Key words and phrases. Invariant tori; quasi-periodically forced system; normal hyperbolicity; Fourier methods; computer-assisted proof; INVARIANT TORI; PARAMETERIZATION METHOD; ASYMPTOTIC STABILITY; COMPUTATION; WHISKERS; MAPS; EXPLORATIONS; MECHANISMS;

D O I：

10.3934/dcdsb.2024143

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. The goal of this paper is to provide a methodology to prove the existence of (fiberwise hyperbolic) real-analytic invariant tori in real-analytic quasi-periodic skew-product dynamical systems that present nearly-invariant tori of the same characteristics. The methodology was based on the application of a Newton-Kantorovich theorem whose hypotheses were tested using Fourier analysis methods for a numerical approximation of the parameterization of an invariant torus.

引用

页数：22

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