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DCDS

We present a topological method of obtaining the existence of
infinite number of symmetric periodic orbits for systems with
reversing symmetry. The method is based on covering relations. We
apply the method to a four-dimensional reversible map.

DCDS-B

The four dimensional Rössler system is investigated. For this system the Poincaré map
exhibits chaotic dynamics with two expanding directions and one strongly contracting direction.
It is shown that the 16th iterate of this Poincaré map has a nontrivial invariant set on which it is semiconjugated to the full shift on
two symbols. Moreover, it is proven that there exist infinitely many homoclinic and
heteroclinic solutions connecting periodic orbits of period two and four, respectively.
The proof utilizes the method of covering relations with
smooth tools (cone conditions).

The proof is computer assisted - interval arithmetic is used to obtain bounds of the Poincaré map and its derivative.

The proof is computer assisted - interval arithmetic is used to obtain bounds of the Poincaré map and its derivative.

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