Limit Cycles in Planar Piecewise Linear Hamiltonian Systems with Three Zones Without Equilibrium Points

DOI10.1142/S0218127420501576zbMath1453.34047OpenAlexW3088944815MaRDI QIDQ4971034

Jaume Llibre, Luis Fernando Mello, Alexander Fernandes da Fonseca

Publication date: 8 October 2020

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

Full work available at URL: https://doi.org/10.1142/s0218127420501576

zbMATH Keywords

limit cycleHamiltonian vector fieldpiecewise smooth vector field

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) Discontinuous ordinary differential equations (34A36)

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Limit Cycles in Discontinuous Piecewise Linear Planar Hamiltonian Systems Without Equilibrium Points ⋮ Limit Cycles of Planar Discontinuous Piecewise Linear Hamiltonian Systems Without Equilibria Separated by Nonregular Curves ⋮ Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones ⋮ Limit cycles of planar picewise linear Hamiltonian systems without equilibrium points separated by two circles ⋮ Global dynamics of a degenerate planar piecewise linear differential system with three zones ⋮ Unnamed Item ⋮ Limit cycles in the discontinuous planar piecewise linear systems with three zones ⋮ Bifurcation of limit cycles in a piecewise smooth near-integrable system ⋮ Bifurcation of periodic orbits and its application for high-dimensional piecewise smooth near integrable systems with two switching manifolds ⋮ Persistence of periodic solutions from discontinuous planar piecewise linear Hamiltonian differential systems with three zones

Cites Work

• Uniqueness and non-uniqueness of limit cycles for piecewise linear differential systems with three zones and no symmetry
• Piecewise linear differential systems with only centers can create limit cycles?
• Piecewise linear differential systems without equilibria produce limit cycles?
• Phase portraits of continuous piecewise linear Liénard differential systems with three zones
• Jump bifurcations in some degenerate planar piecewise linear differential systems with three zones
• Piecewise-smooth dynamical systems. Theory and applications
• LIMIT CYCLES FOR A CLASS OF CONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH THREE ZONES
• BIFURCATION SETS OF SYMMETRICAL CONTINUOUS PIECEWISE LINEAR SYSTEMS WITH THREE ZONES
• Limit Cycles Bifurcating from a Period Annulus in Continuous Piecewise Linear Differential Systems with Three Zones
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