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Averaging based methods for dectecting invariant compact sets

Abstract

The objective of this project is to expand the theoretical basis of results, involving the averaging theory for detection of compact invariant sets, which was developed by me and other collaborators in recent years. Our results propose a change in the so-called "classical averaging method for detection of periodic orbits", and may reveal a class of orbits that cannot be detected by the classical approach. Additionally, we will apply recently obtained results for the detection of invariant tori in various important systems. For this, we will essentially use two approaches. The first consists of relating the periodic orbits of the truncated averaged system with the invariant tori in the original system. The second consists of studying the degenerate Neimark-Sacker bifurcations in systems in the standard form of averaging theory, via calculation of the Lyapunov coefficients of the truncated averaged system. (AU)

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