In this paper, we investigate the existence of random absolutely continuous invariant measures (ACIP) for expanding on average Saussol maps in higher dimensions. This is done by establishment a Lasota–Yorke inequality transfer operators space bounded oscillation. We prove that number ergodic skew product ACIPs finite and will provide an upper bound these ACIPs. work can be seen as generalizatio...

We describe the transfer operator approach to coupled map lattices (CML) in cases where the local map is expanding but has no Markov partition (e.g. a general tent map). The coupling is allowed to be non-local, but the total innuence of all sites j 6 = i on site i must be small. The main technical tool are lattice-size independent estimates of Lasota-Yorke type which show that the transfer (Per...

Heyl (2000) made an interesting suggestion that the observed shifts in QPO frequency in type I X-ray bursts could be influenced by the same geometrical effect of strong gravity as the one that causes centrifugal force reversal discovered by Abramowicz and Lasota (1974). However, his main result contains a sign error. Here we derive the correct formula and conclude that constraints on the M(R) r...

In this paper, several sufficient conditions are established for the global stability of the positive steady state of a scalar functional differential equation x′ = −Lxt + f(xt), x ≥ 0 (1). The basic idea of the paper is to reduce an infinite dimensional system generated by (1) in some “friendly” spaces to the study of associated one-dimensional maps. In this way, we improve earlier results con...