Continuous orbital invariants of integrable Hamiltonian systems
- Authors: Kudryavtseva E.A.1
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Affiliations:
- Faculty of Mechanics and Mathematics
- Issue: Vol 38, No 6 (2017)
- Pages: 1027-1041
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/200522
- DOI: https://doi.org/10.1134/S199508021706004X
- ID: 200522
Cite item
Abstract
We study integrable Hamiltonian systems with 2 degrees of freedom on regular compact isoenergy 3-manifolds. Such a system is given by a pair (B,F) of a closed 2-form B without zeros and a Bott function F (called the first integral) with dF ∧ B = 0 on a compact 3-manifold Q endowed with a volume form. We prove that, under some additional assumptions, any continuous orbital invariant of integrable systems is “trivial”, i.e. it can be expressed in terms of local extremes of rotation functions on one-parameter families of invariant tori, provided that the systems admit a cross-section of genus 0. We also show which of nontrivial orbital invariants are continuous in the genus 1 case.
About the authors
E. A. Kudryavtseva
Faculty of Mechanics and Mathematics
Author for correspondence.
Email: eakudr@mech.math.msu.su
Russian Federation, Moscow, 119991