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Construction of quasi-periodic response solutions in forced strongly dissipative systems
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Guido Gentile
Published/Copyright:
June 29, 2012
Abstract.
We consider a class of ordinary differential equations describing one-dimensional quasi-periodically forced systems in the presence of large damping. We give a fully constructive proof of the existence of response solutions, that is quasi-periodic solutions which have the same frequency vector as the forcing. This requires dealing with a degenerate implicit function equation: we prove that the latter has a unique solution, which can be explicitly determined. As a by-product we obtain an explicit estimate of the minimal size of the damping coefficient.
Keywords: Dissipative systems; quasi-periodically forced systems; response solution; renormalisation group; divergent series; Bryuno condition
Received: 2010-02-12
Revised: 2010-06-09
Published Online: 2012-06-29
Published in Print: 2012-07-01
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Dissipative systems;
quasi-periodically forced systems;
response solution;
renormalisation group;
divergent series;
Bryuno condition
Articles in the same Issue
- Masthead
- Representations of quivers over a ring and the Weak Krull–Schmidt Theorems
- Logarithmically improved regularity criteria for the 3D viscous MHD equations
- Tilting modules and universal localization
- A bound on the degree of schemes defined by quadratic equations
- Hardy's inequality in the scope of Dirichlet forms
- On some Banach spaces of martingales associated with function spaces
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- On the description of Leibniz superalgebras of nilindex
- Presentations of graph braid groups
- On the vanishing of the lower K-theory of the holomorph of a free group on two generators
- Boundedly generated subgroups of finite groups
