Volume 6, Number 4, 2016, Pages 950967 DOI：10.11948/2016062 
AffinePeriodic Solutions and Pseudo AffinePeriodic Solutions for Differential Equations with Exponential Dichotomy and Exponential Trichotomy 
Cheng Cheng,Fushan Huang,Yong Li 
Keywords:Exponential dichotomy, exponential trichotomy, affineperiodic solutions, pseudo affineperiodic solutions. 
Abstract: 
It is proved that every $(Q,T)$affineperiodic differential equation has a $(Q,T)$affineperiodic solution if the corresponding homogeneous linear equation admits exponential dichotomy or exponential trichotomy. This kind of ``periodic'' solutions might be usual periodic or quasiperiodic ones if $Q$ is an identity matrix or orthogonal matrix. Hence solutions also possess certain symmetry in geometry. The result is also extended to the case of pseudo affineperiodic solutions. 
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