Formulas for the Lyapunov dimension of attractors of the generalized Lorenz system

DOI10.1134/S1064562413030010zbMath1300.37025OpenAlexW2170759019MaRDI QIDQ378181

Gennady Alekseevich Leonov

Publication date: 11 November 2013

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562413030010

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Attractors of solutions to ordinary differential equations (34D45) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dimension theory of smooth dynamical systems (37C45)

Related Items (15)

Development of concept of topological entropy for systems with multiple time ⋮ Further results on ultimate bound on the trajectories of the Lorenz system ⋮ Lyapunov dimension formula for the attractor of the Glukhovsky-Dolzhansky system ⋮ On differences and similarities in the analysis of Lorenz, Chen, and Lu systems ⋮ Exact Lyapunov dimension of attractors and convergence for the Lorenz system ⋮ Necessary and sufficient conditions of the existence of homoclinic trajectories and cascade of bifurcations in Lorenz-like systems: birth of strange attractor and 9 homoclinic bifurcations ⋮ Lyapunov dimension formulas for Lorenz-like systems ⋮ Estimates of the Lyapunov dimension of attractors for generalized Rössler systems ⋮ Qualitative analysis of a new Lorenz-type chaotic system and its simulation ⋮ Lyapunov dimension formula for the global attractor of the Lorenz system ⋮ On estimations of the generalized Hausdorff dimension ⋮ Rössler systems: estimates for the dimension of attractors and homoclinic orbits ⋮ On a model of the dynamical systems describing convective fluid motion in rotating cavity ⋮ Lyapunov functions in the global analysis of chaotic systems ⋮ Unnamed Item

Cites Work

• The dimension formula for the Lorenz attractor
• Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Formulas for the Lyapunov dimension of attractors of the generalized Lorenz system