Computer assisted method for proving existence of periodic orbits

Paweł Pilarczyk

DOI: http://dx.doi.org/10.12775/TMNA.1999.019

Abstract


We introduce a method based on the Conley index theory
for proving the existence of a periodic trajectory
in a smooth dynamical system in $\mathbb R^n$
where an attracting periodic orbit is numerically observed.
We apply this method to prove the existence of a periodic orbit
in the Rössler equations, as announced in [< i> Computer assisted proof of the existence of a periodic orbit in
the Rössler equations< /i> ].

Keywords


Conley index; periodic orbit; Rössler equations; isolating neighbourhood; algorithm

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