Upper bounds for the Hausdorff dimension and stratification of an invariant set of an evolution system on a Hilbert manifold

DOI10.1134/S0012266117130031zbMath1392.37086OpenAlexW2793836936MaRDI QIDQ1643930

A. E. Malykh, A. V. Kruk, Volker Reitmann

Publication date: 20 June 2018

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266117130031

zbMATH Keywords

Hausdorff dimensionsine-Gordon equationWhitney stratificationDouady-Oesterlé theorem

Mathematics Subject Classification ID

Variational inequalities (49J40) Fractals (28A80) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05) Variational principles of physics (49S05)

Related Items (2)

Existence and dimension properties of a global \(\mathcal B\)-pullback attractor for a cocycle generated by a discrete control system ⋮ Contraction analysis of Volterra integral equations via realization theory and frequency-domain methods

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations
• The Lyapunov dimension and its estimation via the Leonov method
• Attractors for damped nonlinear hyperbolic equations
• A two-dimensional mapping with a strange attractor
• Critical point theory and Hamiltonian systems
• Infinite-dimensional dynamical systems in mechanics and physics
• Hausdorff dimension of invariant sets for random dynamical systems
• The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles
• Computer algebra methods for equivariant dynamical systems
• Lyapunov dimension formula for the global attractor of the Lorenz system
• Algebraic approximation of attractors of dynamical systems on manifolds
• Tangents to an analytic variety
• Single-input observability of continuous-time systems
• On the Observability of Polynomial Systems, I: Finite-Time Problems
• Deterministic Nonperiodic Flow
• Cylindrical Algebraic Decomposition I: The Basic Algorithm
• Singular Points of Complex Hypersurfaces. (AM-61)

This page was built for publication: Upper bounds for the Hausdorff dimension and stratification of an invariant set of an evolution system on a Hilbert manifold