Obstructions to shadowing when a Lyapunov exponent is near zero

SILVINA DAWSON; CELSO GREBOGI; TIMOTHY SAUER; JAMES A. YORKE

PHYSICAL REVIEW LETTERS

Año: 1994 vol. 73 p. 1927 - 1930

0031-9007

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 of 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.