1. Computation of Quasiperiodic Normally Hyperbolic Invariant Tori: Rigorous Results.
- Author
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Canadell, Marta and Haro, Àlex
- Subjects
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OSCILLATIONS , *INVARIANTS (Mathematics) , *DYNAMICAL systems , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICAL models - Abstract
The development of efficient methods for detecting quasiperiodic oscillations and computing the corresponding invariant tori is a subject of great importance in dynamical systems and their applications in science and engineering. In this paper, we prove the convergence of a new Newton-like method for computing quasiperiodic normally hyperbolic invariant tori carrying quasiperiodic motion in smooth families of real-analytic dynamical systems. The main result is stated as an a posteriori KAM-like theorem that allows controlling the inner dynamics on the torus with appropriate detuning parameters, in order to obtain a prescribed quasiperiodic motion. The Newton-like method leads to several fast and efficient computational algorithms, which are discussed and tested in a companion paper (Canadell and Haro in J Nonlinear Sci, 2017. doi:), in which new mechanisms of breakdown are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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