Periodic orbits in R\"ossler system

TL;DR

This paper proves the existence of periodic orbits in the Rössler system for most natural numbers, using computer-assisted methods, for two specific parameter sets.

Contribution

It provides the first rigorous proof of the existence of n-periodic orbits in the Rössler system for a wide range of n, using computer-assisted techniques.

Findings

Existence of n-periodic orbits for almost all n in the Rössler system.

Applicable to two parameter sets with attracting periodic orbits.

Proofs are computer-assisted, ensuring rigor.

Abstract

We prove the existence of $n$-periodic orbits for almost all $n\in\mathbb{N}$ in the R\"ossler system with attracting periodic orbit, for two sets of parameters. The proofs are computer-assisted.