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PROC

We discuss an application of a topological-numerical method for proving
the existence of a periodic trajectory in a smooth dynamical system in $\mathbb(R)^n$ where
a periodic trajectory is numerically observed. The method is based on the Conley
index theory and rigorous numerics for ODEs and it is a generalization of the method
introduced in [13]. We apply this method to the Rössler equations.

keywords:
algorithm.
,
periodic orbit
,
Conley index
,
RÃ„ossler equations
,
isolating neighbor-hood

DCDS

We prove that shadowing (the pseudo-orbit tracing property),
periodic shadowing (tracing periodic pseudo-orbits
with periodic real trajectories),
and inverse shadowing with respect to certain families of methods
(tracing all real orbits of the system
with pseudo-orbits generated by arbitrary methods from these families)
are all generic in the class of continuous maps
and in the class of continuous onto maps on compact topological manifolds
(with or without boundary) that admit a decomposition
(including triangulable manifolds and manifolds with handlebody).

## Year of publication

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