Existence of almost periodic solutions of discrete time equations

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January 2001, 7(1): 51-60. doi: 10.3934/dcds.2001.7.51

Existence of almost periodic solutions of discrete time equations

1.	CERMSEM, M.S.E., Université de Paris 1, 106-112 bd de l'Hôpital, 75647 PARIS Cedex 13, France

Received June 2000 Published November 2000

Abstract
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In this paper, we study almost periodic (a.p.) solutions of discrete dynamical systems. We first adapt some results on a.p. differential equations to a.p. difference equations, on the link between boundedness of solutions and existence of a.p. solutions. After, we obtain an existence result in the space of the Harmonic Synthesis for an equation $A_t (x_t,...,x_{t+p})=0$ when the dependance of $A$ on $t$ is a.p. and when $A_t$ and $D A_t$ are uniformly Lipschitz and satisfy another condition which is exactly the extension of a simple one for the basic linear system. The main tools for that are Nonlinear Functional Analysis and the Newton method.

Keywords: bounded solutions, almost periodic solutions, Newton’s method., Discrete Time Equations.

Mathematics Subject Classification: 39A10, 43A60, 93C5.

Citation: Denis Pennequin. Existence of almost periodic solutions of discrete time equations. Discrete & Continuous Dynamical Systems - A, 2001, 7 (1) : 51-60. doi: 10.3934/dcds.2001.7.51

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