Journal
JOURNAL OF NONLINEAR SCIENCE
Volume 27, Issue 6, Pages 1869-1904Publisher
SPRINGER
DOI: 10.1007/s00332-017-9389-y
Keywords
Normally hyperbolic invariant manifolds; KAM theory; Computational dynamical systems
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Funding
- Spanish Grants [MTM2012-32541, MTM2015-67724-P]
- Catalan Grant [2014-SGR-1145]
- FPI [BES-2010-039663]
- NSF [DMS-1500943]
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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:10.1007/s00332-017-9388-z), in which new mechanisms of breakdown are presented.
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