From one-dimensional to infinite-dimensional dynamical systems: Ideal turbulence

DOI10.1007/BF02375370zbMath0936.37021MaRDI QIDQ1962267

E. Yu. Romanenko, O. M. Sharkovs'kyi

Publication date: 22 May 2000

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

coherent structurescascade processrandom functionsself-stochasticityturbulence-first

Mathematics Subject Classification ID

Additive difference equations (39A10) Generation, random and stochastic difference and differential equations (37H10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15)

Related Items (6)

FROM BOUNDARY VALUE PROBLEMS TO DIFFERENCE EQUATIONS: A METHOD OF INVESTIGATION OF CHAOTIC VIBRATIONS ⋮ Randomness in deterministic difference equations ⋮ Ideal turbulence ⋮ Trajectories of intervals in one-dimensional dynamical systems ⋮ Dynamical Systems Induced by Continuous Time Difference Equations and Long-time Behavior of Solutions ⋮ Dynamic boundary conditions in the interface modeling of binary alloys

Cites Work

• The universal metric properties of nonlinear transformations
• Generic hyperbolicity in the logistic family
• Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
• Simulation of spatial-temporal chaos: The simplest mathematical patterns and computer graphics
• Quantitative universality for a class of nonlinear transformations
• On the nature of turbulence
• Period Three Implies Chaos
• IDEAL TURBULENCE IN AN IDEALIZED TIME-DELAYED CHUA’S CIRCUIT
• MINIMAL AND STRANGE ATTRACTORS
• IDEAL TURBULENCE: ATTRACTORS OF DETERMINISTIC SYSTEMS MAY LIE IN THE SPACE OF RANDOM FIELDS
• DRY TURBULENCE AND PERIOD-ADDING PHENOMENA FROM A 1-D MAP WITH TIME DELAY
• SELF-STRUCTURING AND SELF-SIMILARITY IN BOUNDARY VALUE PROBLEMS
• UNIVERSAL PHENOMENA IN SOME INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS
• Universal Phenomena in Solution Bifurcations of Some Boundary Value Problems
• Chaos from a time-delayed Chua's circuit
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: From one-dimensional to infinite-dimensional dynamical systems: Ideal turbulence