Traveling waves in lattice models of multidimensional and multicomponent media. II. Ergodic properties and dimension

DOI10.1063/1.165996zbMath1055.37584OpenAlexW2081727983WikidataQ52397539 ScholiaQ52397539MaRDI QIDQ4526272

Ya. B. Pesin, Valentin Afraimovich, Arkady Tempelman

Publication date: 16 January 2001

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.165996

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Partial differential equations of mathematical physics and other areas of application (35Q99) Hydrodynamic stability (76E99) Dynamical systems approach to turbulence (76F20) Dynamical systems with hyperbolic orbits and sets (37D05) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60)

Related Items (7)

ABUNDANCE OF TRAVELING WAVES IN COUPLED CIRCLE MAPS ⋮ Topological spatial chaos and homoclinic points of \(\mathbb{Z} ^ d\)-actions in lattice dynamical systems ⋮ Stable stationary solutions for a reaction-diffusion equation with a multi-stable nonlinearity ⋮ Wavelengths distribution of chaotic travelling waves in some cellular automata. ⋮ Coupled map lattices: some topological and ergodic properties ⋮ Chaotic invariant sets of high-dimensional Hénon-like maps ⋮ Traveling waves in lattice dynamical systems

Cites Work

• Traveling waves of infinitely many pulses in nerve equations
• The ergodic theorem
• Dimension, entropy and Lyapunov exponents
• Hyperbolicity of infinite-dimensional drift systems
• Ergodic theory of chaos and strange attractors

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