Persistence of cycles and nonhyperbolic dynamics at heteroclinic bifurcations
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Publication:4851037
DOI10.1088/0951-7715/8/5/003zbMath0836.58031OpenAlexW2015703520MaRDI QIDQ4851037
Publication date: 8 May 1996
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1088/0951-7715/8/5/003
Stability theory for smooth dynamical systems (37C75) Local and nonlocal bifurcation theory for dynamical systems (37G99)
Related Items (18)
Persistent homoclinic tangencies and the unfolding of cycles ⋮ Skew product cycles with rich dynamics: From totally non-hyperbolic dynamics to fully prevalent hyperbolicity ⋮ Hopf-homoclinic bifurcations and heterodimensional cycles ⋮ Robust tangencies of large codimension ⋮ Growth of number of periodic orbits of one family of skew product maps ⋮ Non-critical saddle-node cycles and robust non-hyperbolic dynamics ⋮ Hénon-Like Families and Blender-Horseshoes at Nontransverse Heterodimensional Cycles ⋮ Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points ⋮ Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms ⋮ BIFURCATIONS OF 2-2-1 HETERODIMENSIONAL CYCLES UNDER TRANSVERSALITY CONDITION ⋮ Existence of heterodimensional cycles near shilnikov loops in systems with a \(\mathbb{Z}_2\) symmetry ⋮ Coexistence of infinitely many attractors in a simple flow ⋮ Singular cycles of vector fields on regular parts of the boundary of Morse-Smale systems ⋮ Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors ⋮ Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes ⋮ Newhouse phenomenon and homoclinic classes ⋮ Partial hyperbolicity and robust transitivity ⋮ Fast growth of the number of periodic points arising from heterodimensional connections
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