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On instability of minimal foliations for a variational problem on T 2

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Nonlinear Dynamical Systems and Chaos

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 19))

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Abstract

In this paper, we study the variational problem \( \int {F(t,{\kern 1pt} x,{\kern 1pt} {x_t})dt} \), where F(t, x, p) ∊ C r (S 1 × S 1 × R). Suppose x = U(t, αt + 3) is its T-invariant minimal foliation and α does not satisfy Diophantine condition, then we can destroy this minimal foliation by a small C r-perturbation of F(t,x,p).

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Author information

Authors and Affiliations

  1. Faculty of Technical Mathematics and Informatics, Delft University of Technology, 2628 CD, Delft, The Netherlands

    Xianhua Huang

Authors
  1. Xianhua Huang
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computer Science, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands

    H. W. Broer , I. Hoveijn  & F. Takens ,  & 

  2. Faculty of Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    S. A. van Gils

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© 1996 Springer Basel AG

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Huang, X. (1996). On instability of minimal foliations for a variational problem on T 2 . In: Broer, H.W., van Gils, S.A., Hoveijn, I., Takens, F. (eds) Nonlinear Dynamical Systems and Chaos. Progress in Nonlinear Differential Equations and Their Applications, vol 19. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7518-9_17

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  • DOI: https://doi.org/10.1007/978-3-0348-7518-9_17

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-7520-2

  • Online ISBN: 978-3-0348-7518-9

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