Integrable Hamiltonian Systems
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Organizer(s): |
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Affiliation:
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Country:
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Holger Waalkens
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University of Groningen
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Netherlands
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Konstantinos Efstathiou
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Duke Kunshan University
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Peoples Rep of China
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Introduction:
| | Integrable Hamiltonian systems form a special class within Hamiltonian dynamics, characterized by the existence of the maximal number of independent, Poisson-commuting integrals of motion. According to the Arnold–Liouville–Mineur theorem, the regular fibres of the integral map are tori that admit action–angle variables and carry quasi-periodic motions. Beyond their intrinsic geometric richness, integrable systems provide a foundation for understanding general Hamiltonian dynamics, perturbation theory, and semiclassical quantization.
In recent years, attention has increasingly focused on the global and geometric aspects of integrable systems, particularly the structure of their typically singular torus fibrations. Phenomena such as Hamiltonian monodromy reveal the nontrivial topology of these fibrations and play a key role in current classification efforts.
This special session will bring together experts working on various aspects of integrable Hamiltonian systems, including topological and symplectic invariants, singularities, monodromy and its variants, and related developments in symplectic and Poisson geometry. The session aims to highlight recent progress, foster interaction between different approaches, and identify new directions for future research.
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