Time-Reversibility in 2-Dimensional Systems

DOI10.1142/S1230161208000249zbMath1188.70055arXivmath/0702478MaRDI QIDQ3567161

Valery G. Romanovski

Publication date: 11 June 2010

Published in: Open Systems & Information Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702478

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Hamiltonian and Lagrangian mechanics (70H99)

Related Items (15)

On the fixed points set of differential systems reversibilities ⋮ Integrability Conditions for Complex Homogeneous Kukles Systems ⋮ Symbolic computation and the cyclicity problem for singularities ⋮ THE CENTER-FOCUS PROBLEM AND BIFURCATION OF LIMIT CYCLES IN A CLASS OF 7TH-DEGREE POLYNOMIAL SYSTEMS ⋮ Every period annulus is both reversible and symmetric ⋮ Measure-preserving symmetries and reversibilities of ordinary differential systems ⋮ Center conditions and cyclicity for a family of cubic systems: computer algebra approach ⋮ CENTER CONDITIONS FOR THREE CLASSES OF POINCARÉ SYSTEMS IN THE COMPLEX DOMAIN ⋮ Generalized involutive symmetry and its application in integrability of differential systems ⋮ Linearizability conditions of a time-reversible quartic-like system ⋮ Characterizing orbital-reversibility through normal forms ⋮ The Cyclicity of a Cubic System ⋮ Reversibility in polynomial systems of ODE's ⋮ BIFURCATION OF LIMIT CYCLES AND ISOCHRONOUS CENTERS FOR A QUARTIC SYSTEM ⋮ Bifurcation of critical periods of polynomial systems

Cites Work

• Localization and primary decomposition of polynomial ideals
• Time-reversal symmetry in dynamical systems: a survey
• Algebraic properties of the Lyapunov and period constants
• The Sibirsky component of the center variety of polynomial differential systems.
• A class of reversible cubic systems with an isochronous center
• The period function of reversible quadratic centers
• Isochronous centers of a linear center perturbed by fifth degree homogeneous polynomials
• Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in \(\mathbb C^2\)
• Poincaré's reversibility condition

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