Obstructions to shadowing when a Lyapunov exponent fluctuates about zero

Journal Article · Mon Oct 03 00:00:00 EDT 1994 · Physical Review Letters; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.73.1927· OSTI ID:7171107

Dawson, S ^[1]; Grebogi, C ^[2]; Sauer, T ^[3]; Yorke, J A ^[4]

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1. Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2. Department of Mathematics, University of Maryland, College Park, Maryland 20742 (United States)
3. Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030 (United States)
4. Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)

We study the existence or nonexistence of true trajectories of chaotic dynamical systems that lie close to computer-generated trajectories. The nonexistence of such shadowing trajectories is caused by finite-time Lyapunov exponents of the system fluctuating about zero. A dynamical mechanism for the unshadowability is explained through a theoretical model and identified in simulations of a typical physical system. The problem of fluctuating Lyapunov exponents is expected to be common in simulations of higher-dimensional systems.

• OSTI ID: 7171107
• Journal Information: Physical Review Letters; (United States), Vol. 73:14; ISSN 0031-9007
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
STOCHASTIC PROCESSES
ATTRACTORS
COMPUTERS
FLUCTUATIONS
LYAPUNOV METHOD
MATHEMATICAL MODELS
SIMULATION
CALCULATION METHODS
VARIATIONS
661100* - Classical & Quantum Mechanics- (1992-)