KNEADINGS, SYMBOLIC DYNAMICS AND PAINTING LORENZ CHAOS
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Publication:4908754
DOI10.1142/S0218127412300169zbMath1258.37035arXiv1204.3278MaRDI QIDQ4908754
Roberto Barrio, Andrej L. Shil'nikov, L. P. Shil'nikov
Publication date: 6 March 2013
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1204.3278
Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Topological entropy (37B40) Symbolic dynamics (37B10) Ergodic theory (37A99) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)
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Cites Work
- Unnamed Item
- Bifurcations of an optically pumped three-level laser model
- Bounds for the chaotic region in the Lorenz model
- A three-parametric study of the Lorenz model
- Compound windows of the Hénon-map
- Local and global behavior near homoclinic orbits
- Bifurcation phenomena near homoclinic systems: A two-parameter analysis
- T-points: A codimension two heteroclinic bifurcation
- Structural stability of Lorenz attractors
- Preturbulence: A regime observed in a fluid flow model of Lorenz
- On bifurcations of the Lorenz attractor in the Shimizu-Morioka model
- The bifurcations of separatrix contours and chaos
- Splitting words and Lorenz braids
- Mathematical problems of nonlinear dynamics: A tutorial
- T-points in a \(\mathbb Z_2\)-symmetric electronic oscillator. I: Analysis
- Qualitative analysis of the Rössler equations: bifurcations of limit cycles and chaotic attractors
- Homoclinic bifurcation to a transitive attractor of Lorenz type
- THE STRUCTURE OF INFINITE PERIODIC AND CHAOTIC HUB CASCADES IN PHASE DIAGRAMS OF SIMPLE AUTONOMOUS FLOWS
- The topological classification of Lorenz attractors
- CHUA’S CIRCUIT: RIGOROUS RESULTS AND FUTURE PROBLEMS
- ON THE NONSYMMETRICAL LORENZ MODEL
- NORMAL FORMS AND LORENZ ATTRACTORS
- An example of a wild strange attractor
- Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits
- Deterministic Nonperiodic Flow
- SMOOTH SYMMETRIC AND LORENZ MODELS FOR UNIMODAL MAPS
- THREE-DIMENSIONAL HÉNON-LIKE MAPS AND WILD LORENZ-LIKE ATTRACTORS
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