Continuous orbital invariants of integrable Hamiltonian systems
- Авторы: Kudryavtseva E.1
-
Учреждения:
- Faculty of Mechanics and Mathematics
- Выпуск: Том 38, № 6 (2017)
- Страницы: 1027-1041
- Раздел: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/200522
- DOI: https://doi.org/10.1134/S199508021706004X
- ID: 200522
Цитировать
Аннотация
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.
Об авторах
E. Kudryavtseva
Faculty of Mechanics and Mathematics
Автор, ответственный за переписку.
Email: eakudr@mech.math.msu.su
Россия, Moscow, 119991