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Stability Analysis of Numerically Approximated Quasiperiodic Motions
Author(s) -
Fiedler Robert,
Hetzler Hartmut
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800189
Subject(s) - quasiperiodic function , lyapunov exponent , invariant (physics) , mathematics , mathematical analysis , stability (learning theory) , lyapunov function , interval (graph theory) , manifold (fluid mechanics) , invariant manifold , physics , mathematical physics , quantum mechanics , computer science , combinatorics , nonlinear system , machine learning , mechanical engineering , engineering
This contribution deals with the stability analysis of flows on invariant manifolds based on the theory of LYAPUNOV‐exponents. The description using an invariant manifold for quasiperiodic motions allows an analysis of a finite p ‐dimensional interval instead of an investigation through time integration of an one dimensional infinite interval. To demonstrate the use of this approach the LYAPUNOV‐exponents are calculated for a quasiperiodic motion of a forced VAN‐DER‐POL equation. The verification of the proposed method is carried out by comparing the results to an alternative approach based on a time integration using a continuous GRAM‐SCHMIDT orthonormalization.