Symplectic geometry of the Koopman operator

DOI10.1134/S1064562421040104zbMath1483.37077OpenAlexW3201539190MaRDI QIDQ2246875

Yanyan Li

Publication date: 16 November 2021

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562421040104

zbMATH Keywords

ergodicitydiscrete spectrumsymplectic structureLebesgue spectrumKoopman operatorquadratic invariants

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Symplectic and canonical mappings (37J11) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Cites Work

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• On the ergodic theory of equations of mathematical physics
• Symplectic geometry of a linear transformation with a quadratic invariant
• Linear system of differential equations with a quadratic invariant as the Schrödinger equation
• On the Hamiltonian property of linear dynamical systems in Hilbert space
• Quadratic conservation laws for equations of mathematical physics

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