DEGENERATE BIFURCATIONS OF HETERODIMENSIONAL CYCLES WITH ORBIT FLIP

DOI10.1142/S0218127413500806zbMath1270.34087OpenAlexW2089532288MaRDI QIDQ2845296

Jun-Ying Liu, De-Ming Zhu, Xing Bo Liu

Publication date: 22 August 2013

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

Full work available at URL: https://doi.org/10.1142/s0218127413500806

zbMATH Keywords

bifurcationlocal coordinatesorbit flipheterodimensional cycle

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (4)

Loop Numbers for the Stability of Homoclinic Loops of Planar Vector Fields ⋮ Dynamics Near the Heterodimensional Cycles with Nonhyperbolic Equilibrium ⋮ Bifurcations of Double Homoclinic Loops in Reversible Systems ⋮ Generic unfolding of a degenerate heterodimensional cycle

Cites Work

• Heteroclinic orbits in slow-fast Hamiltonian systems with slow manifold bifurcations
• Bifurcations of heterodimensional cycles with two saddle points
• Bifurcations of heterodimensional cycles with one orbit flip and one inclination flip
• Branching of double pulse solutions from single pulse solutions in nerve axon equations
• The Sil'nikov problem, exponential expansion, strong \(\lambda\)-lemma, \(C^ 1\)-linearization, and homoclinic bifurcation
• Bifurcations of heteroclinic loops
• Constructing dynamical systems having homoclinic bifurcation points of codimension two
• When gap solitons become embedded solitons: A generic unfolding
• Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in \(\mathbb R^3\)
• Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit
• Generic diffeomorphisms away from homoclinic tangencies and heterodimensional cycles
• Inclination-flip homoclinic orbits arising from orbit-flip
• Numerical unfoldings of codimension-three resonant homoclinic flip bifurcations
• Lorenz attractors in unfoldings of homoclinic-flip bifurcations
• HETERODIMENSIONAL CYCLE BIFURCATION WITH ORBIT-FLIP
• Problems in homoclinic bifurcation with higher dimensions
• Heterodimensional cycles, partial hyperbolicity and limit dynamics
• Resonant homoclinic flip bifurcations

This page was built for publication: DEGENERATE BIFURCATIONS OF HETERODIMENSIONAL CYCLES WITH ORBIT FLIP