Hausdorff dimension estimates for invariant sets of time-dependent vector fields

DOI10.4171/ZAA/710zbMath0923.58029MaRDI QIDQ1915227

Antje Noack, Volker Reitmann

Publication date: 19 October 1999

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

zbMATH Keywords

stabilitydynamical systemHausdorff dimensionBetti numbernegatively invariant setstime-dependent vector fieldsnontrivial periodic orbits

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Applications of dynamical systems (37N99) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Differentiable maps on manifolds (58C25) Partial differential equations (35-XX)

Related Items (8)

Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents ⋮ Hausdorff and fractal dimension estimates for invariant sets of non-injective maps ⋮ Review on contraction analysis and computation of contraction metrics ⋮ Maximum local Lyapunov dimension bounds the box dimension. Direct proof for invariant sets on Riemannian manifolds ⋮ Dimension estimates in smooth dynamics: a survey of recent results ⋮ The Lyapunov dimension and its estimation via the Leonov method ⋮ Asymptotic orbital stability conditions for flows by estimates of singular values of the linearization ⋮ Fractal dimension estimates for invariant sets of non-injective maps

Cites Work

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• Some relations between dimension and Lyapunov exponents
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• Compound matrices and ordinary differential equations
• The problem of Plateau on a Riemannian manifold
• Some applications of Hausdorff dimension inequalities for ordinary differential equations
• A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
• An Improved Closing Lemma and a General Density Theorem

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