Multidimensional Hamiltonian systems: non-integrability and diffusion
- Authors: Kozlov V.V.1
-
Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 80, No 5 (2025)
- Pages: 3-22
- Section: Articles
- URL: https://medbiosci.ru/0042-1316/article/view/331267
- DOI: https://doi.org/10.4213/rm10261
- ID: 331267
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Abstract
Hamiltonian systems of differential equations that are little different from completely integrable systems are under consideration. If such a system is integrable, then the action variables cannot change strongly, and there is no diffusion. Thus the non-integrable behaviour of a Hamiltonian system is closely linked with the diffusion of slow variables. This range of problems is discussed for a subclass of Hamiltonian systems. A new mechanism of diffusion, different from the ‘standard’ scheme of transition chains, is considered on these example. This mechanism is related to the breakdown of a large number of invariant tori of the non-perturbed problem which have almost resonance sets of frequencies. On the formal side, this phenomenon is based on the non-boundedness of integrals of conditionally-periodic functions of time with zero mean.
About the authors
Valery Vasil'evich Kozlov
Steklov Mathematical Institute of Russian Academy of Sciences
Email: vvkozlov@presidium.ras.ru
Scopus Author ID: 7402207934
ResearcherId: Q-4001-2016
Doctor of physico-mathematical sciences, Professor
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