Partial Preservation of Frequencies and Floquet Exponents of Invariant Tori in the Reversible KAM Context 2
| Autor: | Mikhail B. Sevryuk |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Floquet theory Pure mathematics Mathematics::Dynamical Systems General Mathematics Context (language use) Dynamical Systems (math.DS) Fixed point 01 natural sciences 010305 fluids & plasmas 0103 physical sciences FOS: Mathematics Mathematics - Dynamical Systems 0101 mathematics Invariant (mathematics) Mathematics::Symplectic Geometry Mathematics 70K43 70H33 Kolmogorov–Arnold–Moser theorem Applied Mathematics 010102 general mathematics Torus General Medicine Codimension Mathematics::Spectral Theory Manifold |
| Zdroj: | Journal of Mathematical Sciences. 253:730-753 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-021-05265-x |
| Popis: | We consider the persistence of smooth families of invariant tori in the reversible context 2 of KAM theory under various weak nondegeneracy conditions via Herman's method. The reversible KAM context 2 refers to the situation where the dimension of the fixed point manifold of the reversing involution is less than half the codimension of the invariant torus in question. The nondegeneracy conditions we employ ensure the preservation of any prescribed subsets of the frequencies of the unperturbed tori and of their Floquet exponents (the eigenvalues of the coefficient matrix of the variational equation along the torus). 34 pages. The material of Section 4 (included to achieve a self-contained presentation) almost coincides with that of Section 4 in arXiv:1612.07653 |
| Databáze: | OpenAIRE |
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