On the number of limit cycles near a homoclinic loop with a nilpotent cusp of order \(m\)
DOI10.1016/j.jde.2023.10.037OpenAlexW4388439153MaRDI QIDQ6140125
Publication date: 19 January 2024
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2023.10.037
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)
Cites Work
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- Limit cycle bifurcation by perturbing a cuspidal loop of order 2 in a Hamiltonian system
- On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle
- Hopf and homoclinic bifurcations for near-Hamiltonian systems
- Limit cycles near homoclinic and heteroclinic loops
- Estimating the number of limit cycles in polynomial systems
- On the number of zeros of Abelian integrals. A constructive solution of the infinitesimal Hilbert sixteenth problem
- Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
- Melnikov functions for period annulus, nondegenerate centers, heteroclinic and homoclinic cycles.
- Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order \(m\)
- On the Melnikov functions and limit cycles near a double homoclinic loop with a nilpotent saddle of order \(\hat{m} \)
- On the qualitative behavior of a class of generalized Liénard planar systems
- The smallest upper bound on the number of zeros of abelian integrals
- New lower bounds for the Hilbert number of polynomial systems of Liénard type
- Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system
- Bifurcations of small limit cycles in Liénard systems with cubic restoring terms
- The number of small-amplitude limit cycles of Liénard equations
- On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
- Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
- LIMIT CYCLE BIFURCATIONS NEAR A DOUBLE HOMOCLINIC LOOP WITH A NILPOTENT SADDLE
- HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS
- Limit Cycle Bifurcations by Perturbing a Hamiltonian System with a Cuspidal Loop of Order m
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