Hausdorff and fractal dimension estimates for invariant sets of non-injective maps

DOI10.4171/ZAA/816zbMath0896.58042WikidataQ114021359 ScholiaQ114021359MaRDI QIDQ1381132

V. A. Boichenko, Gennady Alekseevich Leonov, Volker Reitmann, Astrid Franz

Publication date: 17 March 1998

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

zbMATH Keywords

upper boundsHausdorff dimensionsingular valuesfractal dimensionstangent mapnon-injective maps

Mathematics Subject Classification ID

Topological dynamics (37B99) Attractors and repellers of smooth dynamical systems and their topological structure (37C70)

Related Items (7)

On differences and similarities in the analysis of Lorenz, Chen, and Lu systems ⋮ Lyapunov functions in the attractor dimension theory ⋮ Maximum local Lyapunov dimension bounds the box dimension. Direct proof for invariant sets on Riemannian manifolds ⋮ Unnamed Item ⋮ Fractal dimension estimate for invariant set in complete Riemannian manifold ⋮ Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor ⋮ Fractal dimension estimates for invariant sets of non-injective maps

Cites Work

• Unnamed Item
• Unnamed Item
• Some relations between dimension and Lyapunov exponents
• Infinite-dimensional dynamical systems in mechanics and physics
• A note on Kaplan-Yorke-type estimates on the fractal dimension of chaotic attractors
• Hausdorff dimension estimates for invariant sets of time-dependent vector fields
• Hausdorff Dimension Estimates for Invariant Sets of Piecewise Smooth Maps
• Local Lyapunov exponents and a local estimate of Hausdorff dimension

This page was built for publication: Hausdorff and fractal dimension estimates for invariant sets of non-injective maps