On the application of normal forms near attracting fixed points of dynamical systems

Tassos Bountis, George Tsarouhas

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

It is shown on an integrable example in the plane, that normal form solutions need not converge over the full basin of attraction of fixed points of dissipative dynamical systems. Their convergence breaks down at a singularity in the complex time plane of the exact solutions of the problem. However, as is demonstrated on a nonintegrable example with 3-dimensional phase space, the region of convergence of normal forms can be large enough to extend almost to a nearby hyperbolic fixed point, whose invariant manifolds "embrace" the attracting fixed point forming a complicated basin boundary. Thus, in such problems, normal forms are shown to be useful in practice, as a tool for finding large regions of initial conditions for which the solutions are necessarily attracted to the fixed point at t → ∞.

Original languageEnglish
Pages (from-to)160-178
Number of pages19
JournalPhysica A: Statistical Mechanics and its Applications
Volume153
Issue number1
DOIs
Publication statusPublished - Nov 1 1988

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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