Communications on Pure and Applied Analysis (CPAA)

Finding invariant tori with Poincare's map

Pages: 433 - 443, Volume 7, Issue 2, March 2008      doi:10.3934/cpaa.2008.7.433

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Hsuan-Wen Su - Department of Mathematics, National Changhua University of Education, 1, Jin-De Rd, Changhua, 50007, Taiwan (email)

Abstract: 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:  semiflow, Poincare's map, weak quasi-periodic family of solutions, Besicovitch almost periodic solutions.
Mathematics Subject Classification:  Primary: 37B55; Secondary: 34C27.

Received: October 2006;      Revised: February 2007;      Available Online: December 2007.