2021/03/26 by Alexander V. Turbiner, Juan Carlos Lopez Vieyra · 4 citations
Mathematics · Physics and Astronomy · #Algebraic function #Algebraic number #Algebraic surface #Bernoulli's principle #Hamiltonian (control theory) #Limit (mathematics) #Planar #Poisson distribution #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #physics.class-ph
paper · pdf · doi:10.1142/s0217751x21501165
published in International Journal of Modern Physics A 36(17), 2150116 (World Scientific) · 16 pages, 14 Figures (23 eps figures)
arxiv created 2021/03/26 · openalex created_date 2021/04/13 · openalex publication_date 2021/06/08 · arxiv updated 2021/10/14 · openalex updated_date 2026/08/05
For one 3-body and two 5-body planar choreographies on the same algebraic lemniscate by Bernoulli we found explicitly a maximal possible set of (particular) Liouville integrals, 7 and 15, respectively, (including the total angular momentum), which Poisson commute with the corresponding Hamiltonian along the trajectory. Thus, these choreographies are particularly maximally superintegrable. It is conjectured that the total number of (particular) Liouville integrals is maximal possible for any odd number of bodies [Formula: see text] moving choreographically (without collisions) along given algebraic lemniscate, thus, the corresponding trajectory is particularly, maximally superintegrable. Some of these Liouville integrals are presented explicitly. The limit [Formula: see text] is studied: it is predicted that one-dimensional liquid with nearest-neighbor interactions occurs, it moves along algebraic lemniscate and it is characterized by infinitely many constants of motion.