 01218 Michael Blank
 PerronFrobenius spectrum for random maps and its approximation
(85K, LATeX 2e)
Jun 20, 01

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. To study the convergence to equilibrium in random
maps we developed the spectral theory of the corresponding transfer
(PerronFrobenius) operators acting in a certain Banach space of
generalized functions. The random maps under study in a sense fill
the gap between expanding and hyperbolic systems since among their
(deterministic) components there are both expanding and contracting
ones. We prove stochastic stability of the PerronFrobenius spectrum
and developed its finite rank operator approximations by means of a
``stochastically smoothed'' Ulam approximation scheme. A counterexample
to the original Ulam conjecture about the approximation of the SBR
measure and the discussion of the instability of spectral approximations
by means of the original Ulam scheme are presented as well.
 Files:
01218.tex