Periodic orbits in the Rössler system

Abstract We prove the existence of n -periodic orbits for almost all n ∈ N in the Rossler system with an attracting periodic orbit, for two sets of parameters. The methods, using covering relations between two-dimensional sets, are similar to the ones used often in the proofs of the Sharkovskii Theorem. The proofs are computer-assisted with the use of C++ library CAPD containing modules for interval arithmetic, differentiation and integration of ODEs.