The explosion of singular cycles

DOI10.1007/BF02712919zbMath0801.58010OpenAlexW1963934010MaRDI QIDQ1324082

Rodrigo Bamón, Rafael Labarca, Ricardo Mañé, José Pacífico

Publication date: 29 November 1994

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_1993__78__207_0

zbMATH Keywords

vector fieldssingular cyclesdepending on a parameter

Mathematics Subject Classification ID

Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Local and nonlocal bifurcation theory for dynamical systems (37G99) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Related Items (21)

ON BIFURCATION SETS FOR SYMBOLIC DYNAMICS IN THE MILNOR–THURSTON WORLD ⋮ Unfolding contracting singular cycles ⋮ A formula for the boundary of chaos in the lexicographical scenario and applications to the bifurcation diagram of the standard two parameter family of quadratic increasing-increasing Lorenz maps ⋮ Lorenz attractor through saddle-node bifurcations ⋮ Nonhyperbolic persistent attractors near the Morse-Smale boundary. ⋮ Bifurcation of contracting singular cycles ⋮ Robust attractors without dominated splitting on manifolds with boundary ⋮ A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical Scenario ⋮ SINGULAR CYCLES AND C^k-ROBUST TRANSITIVE SET ON MANIFOLD WITH BOUNDARY ⋮ On the intersection of sectional-hyperbolic sets ⋮ Singular strange attractors on the boundary of Morse-Smale systems ⋮ A characterization of the kneading sequences associated to Lorenz maps of the interval ⋮ A global perspective for non-conservative dynamics ⋮ Degenerated singular cycles of inclination-flip type1 ⋮ An improved sectional-Anosov closing Lemma ⋮ Singular cycles of vector fields on regular parts of the boundary of Morse-Smale systems ⋮ Lyapunov-Schmidt reduction for unfolding heteroclinic networks of equilibria and periodic orbits with tangencies ⋮ Saddle-focus singular cycles and prevalence of hyperbolicity ⋮ Contracting singular cycles ⋮ Bifurcations of a pair of nonorientable heteroclinic cycles ⋮ ON THE BOUNDARY OF TOPOLOGICAL CHAOS FOR THE MILNOR–THURSTON WORLD

Cites Work

• Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms
• Stability of singular horseshoes
• Structural stability of Lorenz attractors
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
• ON ATTAINABLE TRANSITIONS FROM MORSE-SMALE SYSTEMS TO SYSTEMS WITH MANY PERIODIC MOTIONS
• Unnamed Item

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