Title :
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
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;
Conference_Titel :
Control of Oscillations and Chaos, 2000. Proceedings. 2000 2nd International Conference
Conference_Location :
St. Petersburg
Print_ISBN :
0-7803-6434-1
DOI :
10.1109/COC.2000.873506
