Marginal singularities,almost invariant sets,and small perturbations of chaotic dynamical systems |
| |
Authors: | Blank M L |
| |
Institution: | N. I. Vavilov Institute of General Genetics, USSR Academy of Sciences, Gubkin Street 3, 117809 Moscow B-333, USSR. |
| |
Abstract: | For a class of piecewise monotone locally noncontracting maps f:X-->X with small "traps" Y( varepsilon ) subset, dbl equals X (diam(Y( varepsilon ))= varepsilon ), the existence of smooth conditionally f-invariant measures &mgr;( varepsilon ) are proved, corresponding to a limit as n--> infinity conditional probabilities that f(n+1)x in X\Y( varepsilon ) if x,fx,.,f(nx) in X\Y( varepsilon ) and the point x is chosen at random. Also proven is the convergence of &mgr;( varepsilon ) to smooth f-invariant measures as varepsilon -->0. By means of this construction, the numerical phenomenon of the convergence of histograms of trajectories of maps with marginal singularities to densities of nonfinite smooth invariant measures in the computer modeling was investigated. |
| |
Keywords: | |
本文献已被 PubMed 等数据库收录! |
|