Finding invariant tori with Poincare's map

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March 2008, 7(2): 433-443. doi: 10.3934/cpaa.2008.7.433

Finding invariant tori with Poincare's map

1.	Department of Mathematics, National Changhua University of Education, 1, Jin-De Rd, Changhua, 50007, Taiwan

Received October 2006 Revised February 2007 Published December 2007

Abstract
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We consider the existence problem of invariant tori for quasi-periodic equation. We regard quasi-periodic functions with $n$ frequencies as periodic functions of functions with $n-1$ frequencies, which constitute a function space. Then we define Poincare's return map of a given semiflow on the space whose fixed point corresponds to an invariant torus of the semiflow.

Keywords: Poincare's map, Besicovitch almost periodic solutions., weak quasi-periodic family of solutions, semiflow.

Mathematics Subject Classification: Primary: 37B55; Secondary: 34C2.

Citation: Hsuan-Wen Su. Finding invariant tori with Poincare's map. Communications on Pure & Applied Analysis, 2008, 7 (2) : 433-443. doi: 10.3934/cpaa.2008.7.433

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