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A KAM Theorem for Reversible Systems of Infinite Dimension

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Abstract

For reversible systems of infinite dimension we prove an infinitely dimensional KAM theorem with an application to the network of weakly coupled oscillators of friction. The KAM theorem shows that there are many invariant tori of infinite dimension, and thus many almost periodic solutions, for the reversible systems.

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Authors and Affiliations

  1. Department of Mathematics, Daxian Normal College, Dazhou, 635000, P. R. China

    Shun Qing Chen

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, P. R. China

    Xiao Ping Yuan*

  3. Key Lab of Mathematics for Nonlinear Science (Fudan University), Ministry of Education, Shanghai, 200433, P. R. China

    Xiao Ping Yuan*

Authors
  1. Shun Qing Chen
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  2. Xiao Ping Yuan*
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Correspondence to Shun Qing Chen.

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*Supported by NNSFC and NCET-04-0365, and in part by STCSM-06ZR14014

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Chen, S.Q., Yuan*, X.P. A KAM Theorem for Reversible Systems of Infinite Dimension. Acta Math Sinica 23, 1777–1796 (2007). https://doi.org/10.1007/s10114-005-0887-8

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  • DOI: https://doi.org/10.1007/s10114-005-0887-8

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