Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field

DOI10.1142/S0218127422501164OpenAlexW4283729524WikidataQ114072971 ScholiaQ114072971MaRDI QIDQ5094743

Jaume Llibre, Ting Chen

Publication date: 4 August 2022

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127422501164

zbMATH Keywords

Hamiltonian systemphase portraitnilpotent centerpiecewise smooth system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Hamilton's equations (70H05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Discontinuous ordinary differential equations (34A36) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (2)

On the number of limit cycles of planar piecewise smooth quadratic systems with focus-parabolic type critical point ⋮ Nilpotent center conditions in cubic switching polynomial Liénard systems by higher-order analysis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analytic nilpotent centers as limits of nondegenerate centers revisited
• Isochronicity of centers in a switching Bautin system
• Algebraic and topological classification of the homogeneous cubic vector fields in the plane
• Quadratic Hamiltonian vector fields
• Quadratic systems with center and their perturbations
• The classification of reversible cubic systems with center
• Remarks on ``The classification of reversible cubic systems with center
• The analytic and formal normal form for the nilpotent singularity
• Bifurcation analysis on a class of \(Z_{2}\)-equivariant cubic switching systems showing eighteen limit cycles
• Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields
• Bifurcation of limit cycles at infinity in piecewise polynomial systems
• \(Z_2\)-equivariant linear type bi-center cubic polynomial Hamiltonian vector fields
• Center condition and bifurcation of limit cycles for quadratic switching systems with a nilpotent equilibrium point
• Center conditions in a switching Bautin system
• Dynamics in two nonsmooth predator-prey models with threshold harvesting
• Centers of quasi-homogeneous polynomial differential equations of degree three
• Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields
• Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
• Qualitative theory of planar differential systems
• BIFURCATIONS OF LIMIT CYCLES CREATED BY A MULTIPLE NILPOTENT CRITICAL POINT OF PLANAR DYNAMICAL SYSTEMS
• Algebraic Particular Integrals, Integrability and the Problem of the Center
• Classification of Continuous Flows on 2-Manifolds
• BORDER-COLLISION BIFURCATIONS FOR PIECEWISE SMOOTH ONE-DIMENSIONAL MAPS
• Center-Focus Problem for Discontinuous Planar Differential Equations
• Double Bifurcation of Nilpotent Focus
• THE CENTER PROBLEM FOR DISCONTINUOUS LIÉNARD DIFFERENTIAL EQUATION
• Global Structure of Ordinary Differential Equations in the Plane

This page was built for publication: Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field