Proof of the jacobian conjecture in the two-dimensional case and global isochronous centers of polynomial Hamiltonian differential systems

DOI10.1134/S0012266122060106zbMath1504.37071OpenAlexW4297809938WikidataQ114075310 ScholiaQ114075310MaRDI QIDQ2172452

V. V. Amel'kin

Publication date: 15 September 2022

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266122060106

zbMATH Keywords

Jacobian pairsisochronous global centerreal Hamiltonian system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)

Cites Work

• Isochronicity for several classes of Hamiltonian systems
• Isochronous and strongly isochronous foci of polynomial Liénard systems
• Positive solution of one conjecture in the theory of polynomial isochronous centers of Liénard systems
• The Jacobian conjecture: Reduction of degree and formal expansion of the inverse
• A connection between isochronous Hamiltonian centres and the Jacobian Conjecture
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