On detecting of chaotic dynamics via isolating chains

Leszek Pieniążek

DOI: http://dx.doi.org/10.12775/TMNA.2003.031

Abstract


We show in the paper the method of isolating chains
in proof of chaotic dynamics. It is based on the earlier
notion of an isolating segment but gives more powerful
tool for exploring dynamics of periodic ODE's.
As an application we show that the
processes generated by the equations in the complex plane
$ \dot{z} = {\overline z}^k + e^{i\phi t} {\overline z}$,
where $k\geq 3$ is an odd number and $\phi$ is close to $0$,
has chaotic behaviour.

Keywords


Periodic solutions; chaotic dynamics; fixed point index; isolating segment; isolating chain

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