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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2018, том 23, выпуск 2, страницы 212–225 (Mi rcd319)

Эта публикация цитируется в 3 статьях

Persistence Properties of Normally Hyperbolic Tori

Henk Broera, Heinz Hanßmannb, Florian Wagenerc

a Johann Bernoulli Institute for Mathematics and Computer Science, Rijksuniversiteit Groningen, 9747 AG Groningen, The Netherlands
b Mathematisch Instituut, Universiteit Utrecht, Postbus 80010, 3508 TA Utrecht, The Netherlands
c Center for Nonlinear Dynamics in Economics and Finance (CeNDEF), Amsterdam School of Economics, Universiteit van Amsterdam, Postbus 15867, 1001 NJ Amsterdam, The Netherlands

Аннотация: Near-resonances between frequencies notoriously lead to small denominators when trying to prove persistence of invariant tori carrying quasi-periodic motion. In dissipative systems external parameters detuning the frequencies are needed so that Diophantine conditions can be formulated, which allow to solve the homological equation that yields a conjugacy between perturbed and unperturbed quasi-periodic tori. The parameter values for which the Diophantine conditions are not fulfilled form so-called resonance gaps. Normal hyperbolicity can guarantee invariance of the perturbed tori, if not their quasi-periodicity, for larger parameter ranges. For a 1-dimensional parameter space this allows to close almost all resonance gaps.

Ключевые слова: KAM theory, normally hyperbolic invariant manifold, van der Pol oscillator, Hopf bifurcation, center-saddle bifurcation.

MSC: 37J40 37D10 37G35 37J20

Поступила в редакцию: 18.11.2017
Принята в печать: 09.01.2018

Язык публикации: английский

DOI: 10.1134/S1560354718020065



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