Polynomial and linearized normal forms for almost periodic differential systems | Zendy

Hao Wu | Zendy; Jaume Llibre | Zendy; Weigu Li | Zendy

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Polynomial and linearized normal forms for almost periodic differential systems

Author(s) -

Hao Wu,

Jaume Llibre,

Weigu Li

Publication year - 2015

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2016.36.345

Subject(s) - eigenvalues and eigenvectors , polynomial , domain (mathematical analysis) , differential (mechanical device) , physics , combinatorics , mathematics , pure mathematics , mathematical analysis , mathematical physics , quantum mechanics , thermodynamics

Agraïments: The first author is partially supported by NSFC key program of China (no. 11231001). The MINECO/FEDER grant UNAB13-4E-1604. And the third is supported by NSFC for Young Scientists of China (no. 11001047) and NSF of Jiangsu, China (no. BK20131285).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 neighborhood of a hyperbolic singular point of the system ˙x = ε limT→∞1T∫ 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

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