A degenerate singularity generating geometric Lorenz attractors
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Publication:4854158
DOI10.1017/S0143385700009664zbMath0836.58030MaRDI QIDQ4854158
Hiroshi Kokubu, Hiroe Oka, Freddy Dumortier
Publication date: 29 April 1996
Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)
Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Local and nonlocal bifurcation theory for dynamical systems (37G99)
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Cites Work
- Unnamed Item
- Homoclinic bifurcation at resonant eigenvalues
- Branching of double pulse solutions from single pulse solutions in nerve axon equations
- Structural stability of Lorenz attractors
- Applications of centre manifold theory
- The structure of Lorenz attractors
- Bifurcations to \(N\)-homoclinic orbits and \(N\)-periodic orbits in vector fields
- Lorenz attractors through Šil'nikov-type bifurcation. Part I
- Transitivity and invariant measures for the geometric model of the Lorenz equations
- Homoclinic bifurcation to a transitive attractor of Lorenz type
- Generalized bounded variation and applications to piecewise monotonic transformations
- The Existence of Homoclinic Orbits and the Method of Melnikov for Systems in $R^n$
- Homoclinic and heteroclinic bifurcations of Vector fields
- Homoclinic Bifurcation to a Transitive Attractor of Lorenz Type, II
- The topological classification of Lorenz attractors
- Deterministic Nonperiodic Flow
- Invariant manifolds