The definition and measurement of the topological entropy per unit volume in parabolic PDEs

DOI10.1088/0951-7715/12/3/002zbMath0984.37095arXivmath-ph/9805019OpenAlexW2032209030MaRDI QIDQ4329408

Jean-Pierre Eckmann, Pierre Collet

Publication date: 1 May 2002

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/9805019

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05)

Related Items

Spatial and dynamical chaos generated by reaction-diffusion systems in unbounded domains ⋮ Numerical computation of \(\varepsilon\)-entropy for parabolic equations with analytic solutions ⋮ Directional Metric Entropy and Lyapunov Exponents for Dynamical Systems Generated by Cellular Automata ⋮ Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction diffusion systems in \(\mathbb{R}^n\) ⋮ Map lattices coupled by collisions: hitting time statistics and collisions per lattice unit ⋮ Long-time behavior of solutions and chaos in reaction-diffusion equations ⋮ Topological entropy by unit length for the Ginzburg-Landau equation on the line ⋮ Complexity for extended dynamical systems ⋮ Space–time complexity in Hamiltonian dynamics ⋮ Invariance and computation of the extended fractal dimension for the attractor of CGL on \(\mathbb R\) ⋮ NONPARAMETRIC STATISTICAL MODELING OF SPATIOTEMPORAL DYNAMICS BASED ON RECORDED DATA ⋮ Predictability: a way to characterize complexity ⋮ Multiparameter semigroups and attractors of reaction-diffusion equations in ${\mathbb R}^n$