Ergodic maps with Lyapunov exponent equal to zero

Author

Goloubentsev, Alexander F. ; Anikin, Valery M. ; Arkadaksky, Sergey S.

Author_Institution

Dept. of Comput. Phys., Saratov State Univ., Russia

Volume

1

fYear

2000

fDate

2000

Firstpage

44

Abstract

Some properties of the ergodic maps defined on the finite and infinite intervals, that are characterized by the exact invariant densities and the Lyapunov exponent λ, equal to zero, are studied. The solution of the spectral problem for the Perron-Frobenius operators, corresponding to such maps is found. It is shown that the invariant distributions are the indifferent motionless points of these operators. The examples of conjugated maps with λ=0, including the rational generator of pseudorandom values distributed by Cauchy law, are constructed

Keywords

Lyapunov methods; chaos; Cauchy law; Lyapunov exponent; Perron-Frobenius operators; conjugated maps; ergodic maps; exact invariant densities; finite intervals; indifferent motionless points; infinite intervals; invariant distributions; pseudorandom values; rational generator; spectral problem; Chaos; Concrete; Eigenvalues and eigenfunctions; Mechanical factors; Physics computing; Piecewise linear techniques; Trajectory;

fLanguage

English

Publisher

ieee

Conference_Titel

Control of Oscillations and Chaos, 2000. Proceedings. 2000 2nd International Conference

Conference_Location

St. Petersburg

Print_ISBN

0-7803-6434-1

Type

conf

DOI

10.1109/COC.2000.873506

Filename

873506