Polynomial and linearized normal forms for almost periodic differential systems

Weigu Li; Jaume Llibre; Hao Wu

doi:https://doi.org/10.3934/dcds.2016.36.345

Polynomial and linearized normal forms for almost periodic differential systems

Weigu Li, Jaume Llibre, Hao Wu

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

For almost periodic differential systems x = εf (x,t, ε) with x ∈ C<sup>n</sup>, t ∈ R and ε > 0 small enough, we get a polynomial normal form in a neigh-1 borhood of a hyperbolic singular point of the system x = ε lim T→∞1/T ∫<sup>T</sup><inf>0</inf>f (x, t, 0) dt, if its eigenvalues are in the Poincaré domain. The normal form linearizes if the real part of the eigenvalues are non-resonant.

Original language	English
Pages (from-to)	345-360
Journal	Discrete and Continuous Dynamical Systems
Volume	36
Issue number	1
DOIs	https://doi.org/10.3934/dcds.2016.36.345
Publication status	Published - 1 Jan 2016

Keywords

Almost periodic differential systems
Averaging method
Linearization
Normal form

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abstract = "For almost periodic differential systems x = εf (x,t, ε) with x ∈ Cn, t ∈ R and ε > 0 small enough, we get a polynomial normal form in a neigh-1 borhood of a hyperbolic singular point of the system x = ε lim T→∞1/T ∫T0f (x, t, 0) dt, if its eigenvalues are in the Poincar{\'e} domain. The normal form linearizes if the real part of the eigenvalues are non-resonant.",

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N2 - For almost periodic differential systems x = εf (x,t, ε) with x ∈ Cn, t ∈ R and ε > 0 small enough, we get a polynomial normal form in a neigh-1 borhood of a hyperbolic singular point of the system x = ε lim T→∞1/T ∫T0f (x, t, 0) dt, if its eigenvalues are in the Poincaré domain. The normal form linearizes if the real part of the eigenvalues are non-resonant.

AB - For almost periodic differential systems x = εf (x,t, ε) with x ∈ Cn, t ∈ R and ε > 0 small enough, we get a polynomial normal form in a neigh-1 borhood of a hyperbolic singular point of the system x = ε lim T→∞1/T ∫T0f (x, t, 0) dt, if its eigenvalues are in the Poincaré domain. The normal form linearizes if the real part of the eigenvalues are non-resonant.

KW - Almost periodic differential systems

KW - Averaging method

KW - Linearization

KW - Normal form

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Polynomial and linearized normal forms for almost periodic differential systems

Abstract

Keywords

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