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.
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页数：22
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