Lecture Notes in Integral Invariants and Hamiltonian Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908940295471104 |
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| author | Zubelevich, Oleg |
| author_facet | Zubelevich, Oleg |
| contents | In this methodological review, we discuss the fundamental concepts of the theory of integral invariants. This theory originated with Poincare and Cartan \cite{Koz, Kart} and was further developed by Kozlov \cite{int_K}. We demonstrate how the core ideas of this theory link diverse fields of mathematical physics, such as Hamiltonian dynamics, optics, and hydrodynamics. Particular attention is paid to results that are rarely expounded in standard textbooks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_02878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lecture Notes in Integral Invariants and Hamiltonian Systems Zubelevich, Oleg History and Overview Mathematical Physics 37J06, 34C14, 37C10, 37C60, 34C40 In this methodological review, we discuss the fundamental concepts of the theory of integral invariants. This theory originated with Poincare and Cartan \cite{Koz, Kart} and was further developed by Kozlov \cite{int_K}. We demonstrate how the core ideas of this theory link diverse fields of mathematical physics, such as Hamiltonian dynamics, optics, and hydrodynamics. Particular attention is paid to results that are rarely expounded in standard textbooks. |
| title | Lecture Notes in Integral Invariants and Hamiltonian Systems |
| topic | History and Overview Mathematical Physics 37J06, 34C14, 37C10, 37C60, 34C40 |
| url | https://arxiv.org/abs/2507.02878 |