Combination of exhaustive search and continuation method for the study of sinks in the Hénon map

Abstract-The problem of existence of stable periodic orbits (sinks) for the Hénon map in a neighborhood of classical parameter values is studied numerically. Several parameter values which sustain a sink are found. It is shown rigorously that the sinks exist. Regions of existence in the parameter space of the sinks are located using the continuation method

CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems

We present the CAPD::DynSys library for rigorous numerical analysis of dynamical systems. The basic interface is described together with several interesting case studies illustrating how it can be used for computer-assisted proofs in dynamics of ODEs.Comment: 25 pages, 4 figures, 11 full C++ example