Morse equation of attractors for nonsmooth dynamical systems

DOI10.1016/j.jde.2012.08.035zbMath1263.34079OpenAlexW2074199475MaRDI QIDQ713338

Ailing Qi, De-Sheng Li

Publication date: 26 October 2012

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

Full work available at URL: https://doi.org/10.1016/j.jde.2012.08.035

zbMATH Keywords

Lyapunov functionMorse theorydifferential inclusionattractorEuler numberMorse inequalityMorse equationhomology indexMorse setnonsmooth dynamical system

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Ordinary differential inclusions (34A60) Attractors of solutions to ordinary differential equations (34D45) Index theory for dynamical systems, Morse-Conley indices (37B30)

Related Items (6)

Uniform persistence and Hopf bifurcations in \(\mathbb R_+^n\) ⋮ On the Morse theory of attractors: a functional approach ⋮ Bifurcations and attractor-repeller splittings of non-saddle sets ⋮ Unstable manifold, Conley index and fixed points of flows ⋮ Vibration analysis of nonlinear systems with the bilinear hysteretic oscillator by using incremental harmonic balance method ⋮ Dissonant points and the region of influence of non-saddle sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamics and bifurcations of non-smooth mechanical systems
• A cohomological index of Conley type for multi-valued admissible flows
• Conley type index applied to Hamiltonian inclusions
• Integral manifolds and inertial manifolds for dissipative partial differential equations
• On attractors of multivalued semi-flows and differential inclusions
• Nonsmooth mechanics. Models, dynamics and control.
• Infinite-dimensional dynamical systems in mechanics and physics.
• Non-smooth dynamical systems
• On dynamical properties of general dynamical systems and differential inclusions
• Asymptotic stabilization of coupled oscillators with dry friction by feedback control
• Qualitative properties of trajectories of control systems: a survey
• The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations
• Homotopy index for multivalued flows on sleek sets
• Global and pullback attractors of set-valued skew product flows
• Smooth Morse–Lyapunov Functions of Strong Attractors for Differential Inclusions
• Shape and Conley Index of Attractors and Isolated Invariant Sets
• Existence of optimal strategies for a fire confinement problem
• Morse equations and unstable manifolds of isolated invariant sets
• Shape and Morse theory of attractors
• THE HEAVY BALL WITH FRICTION METHOD, I. THE CONTINUOUS DYNAMICAL SYSTEM: GLOBAL EXPLORATION OF THE LOCAL MINIMA OF A REAL-VALUED FUNCTION BY ASYMPTOTIC ANALYSIS OF A DISSIPATIVE DYNAMICAL SYSTEM
• Dynamical systems, shape theory and the Conley index
• Generalizations of the Chua equations
• Morse Decompositions for General Dynamical Systems and Differential Inclusions with Applications to Control Systems
• Asymptotic behaviour of monotone multi-valued dynamical systems
• Set-valued analysis
• On Conley index theory for non-smooth dynamical systems
• Attractors of multivalued semiflows generated by differential inclusions and their approximations
• On dynamical stability in general dynamical systems
• Dynamics of evolutionary equations

This page was built for publication: Morse equation of attractors for nonsmooth dynamical systems