Viability Kernels and Capture Basins for Analyzing the Dynamic Behavior: Lorenz Attractors, Julia Sets, and Hutchinson’s Maps

DOI10.1007/978-3-7643-8482-1_3zbMath1159.37017OpenAlexW168196124MaRDI QIDQ3525243

Jean-Pierre Aubin, Patrick Saint-Pierre

Publication date: 12 September 2008

Published in: Progress in Nonlinear Differential Equations and Their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-7643-8482-1_3

zbMATH Keywords

fractalsLorenz attractorfluctuationviability kernel

Mathematics Subject Classification ID

Ordinary differential inclusions (34A60) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Fractals (28A80) Dynamical systems with hyperbolic orbits and sets (37D05)

Related Items (1)

Observability by using viability kernels

Cites Work

• Viability theorems for a class of differential-operator inclusions
• Structural stability of Lorenz attractors
• Mutational and morphological analysis. Tools for shape evolution and morphogenesis
• Approximation of the viability kernel
• The Lorenz equations: bifurcations, chaos, and strange attractors
• Fluctuation between subsets of evolutions governed by chaotic systems
• Viability Kernels and Capture Basins of Sets Under Differential Inclusions
• A shooting approach to the Lorenz equations
• Attracteurs de Lorenz de variété instable de dimension arbitraire
• Deterministic Nonperiodic Flow
• Set-valued analysis
• Viability theory
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