Title :
On the convergence of nonstationary solutions of the Perron-Frobenius equation to the invariant density
Author :
Goloubentsev, Alexander F. ; Anikin, Valery M. ; Arkadaksky, Sergey S.
Author_Institution :
Dept. of Comput. Phys., Saratov State Univ., Russia
Abstract :
The generating function for the eigenfunctions of the Frobenius-Perron operator of the chaotic maps that are conjugated (related by invertible differentiable transformations) to the tent (pyramidal) map is found. The nonstationary solutions of the Perron-Frobenius equation are expressed in terms of the eigenfunctions of the Perron-Frobenius operator. In this context the convergence of nonstationary densities to invariant one is analysed. The elements of 0-space of evolution operator are found
Keywords :
chaos; convergence of numerical methods; eigenvalues and eigenfunctions; Frobenius-Perron operator; Perron-Frobenius equation; chaotic maps; eigenfunctions; evolution operator; invariant density; invertible differentiable transformations; nonstationary densities; nonstationary solutions; pyramidal map; tent map; Chaos; Difference equations; Eigenvalues and eigenfunctions; Physics computing; Piecewise linear techniques; Polynomials;
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.2000.873537
