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2 results

  • Bifurcation at infinity for equations in spaces of vector-valued functions

  • Part of
  • P. Diamond, P. E. Kloeden, A. M. Krasnosel'skii, A. V. Pokrovskii
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 63 / Issue 2 / October 1997
    Published online by Cambridge University Press:
    09 April 2009, pp. 263-280
    Print publication:
    October 1997
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  • New existence conditions, under which an index at infinity can be calculated, are given for bifurcations at infinity of asymptotically linear equations in spaces of vector-valued functions. The case where a bounded nonlinearity has discontinuous principal homogeneous part is considered. The results are applied to 2π-periodic problems for two-dimensional systems of ordinary differential equations and to a vector two-point boundary value problem.

  • Expansivity of semi-hyperbolic Lipschitz mappings

  • P. Diamond, P. Kloeden, V. Kozyakin, A. Pokrovskii
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 51 / Issue 2 / April 1995
    Published online by Cambridge University Press:
    17 April 2009, pp. 301-308
    Print publication:
    April 1995
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  • Semi-hyperbolic dynamical systems generated by Lipschitz mappings are shown to be exponentially expansive, locally at least, and explicit rates of expansion are determined. The result is applicable to nonsmooth noninvertible systems such as those with hysteresis effects as well as to classical systems involving hyperbolic diffeomorphisms.