Dynamical systems on infinitely sheeted Riemann surfaces

DOI10.1016/j.physd.2007.02.001zbMath1130.37384arXivnlin/0607028OpenAlexW2123519225MaRDI QIDQ878963

Yuri N. Fedorov, Daivd Gómez-Ullate

Publication date: 4 May 2007

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0607028

zbMATH Keywords

isochronicityRiemann surfacecomplex dynamicssensitive dependenceinversion of hyperelliptic integrals

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical systems over complex numbers (37F99) Riemann surfaces (30F99)

Related Items (10)

Newtonian dynamics in the plane corresponding to straight and cyclic motions on the hyperelliptic curve \(\mu^{2}= \nu^{n}-1, n \in \mathbb Z\): ergodicity, isochrony and fractals ⋮ Complex Classical Motion in Potentials with Poles and Turning Points ⋮ Probability density in the complex plane ⋮ Inversion of hyperelliptic integrals of arbitrary genus with application to particle motion in general relativity ⋮ Understanding complex dynamics by means of an associated Riemann surface ⋮ Isochronous systems and their quantization ⋮ Periodic orbits for classical particles having complex energy ⋮ Asymptotically isochronous systems ⋮ On a generalization of Jacobi's elliptic functions and the double sine-Gordon kink chain ⋮ Inversion of a general hyperelliptic integral and particle motion in Hořava–Lifshitz black hole space-times

Cites Work

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• The analytic structure of dynamical systems and self-similar natural boundaries
• Complete integrability beyond Liouville-Arnol'd
• Integrating the nonintegrable: Analytic structure of the Lorentz system revisited
• Integrable systems and symmetric products of curves
• Double pendulum and \(\theta\)-divisor
• On the weak Kowalevski-Painlevé property for hyperelliptically separable systems
• Reduction of abelian functions and algebraically integrable systems. I
• Newtonian dynamics in the plane corresponding to straight and cyclic motions on the hyperelliptic curve \(\mu^{2}= \nu^{n}-1, n \in \mathbb Z\): ergodicity, isochrony and fractals
• Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians
• Ratio-Like and Recurrence Relation Tests for Convergence of Series
• Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes
• Non-integrable systems with algebraic singularities in complex time
• Periodic Motions Galore: How to Modify Nonlinear Evolution Equations so that They Feature a Lot of Periodic Solutions
• On the connection between hyperelliptic separability and Painlevé integrability
• Periodic Solutions of a Many-Rotator Problem in the Plane. II. Analysis of Various Motions
• Periodic Solutions of a System of Complex ODEs. II. Higher Periods
• Classical trajectories for complex Hamiltonians
• The transition from regular to irregular motions, explained as travel on Riemann surfaces

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