Abstract
We prove the existence of n-periodic orbits for almost all n∈N in the Rössler 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.
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