Pointwise ergodic theorems for maps with indifferent fixed points
by
Tomoki Inoue
Ehime University

We study one dimensional maps T with indifferent fixed points p and q ( p and q are fixed points with T^'(p) = T^'(q) = 1 ) satisfying some conditions. The dynamical systems we mainly consider in this talk have Lebesgue equivalent ergodic infinite invariant measures.

We consider the limit of the ratio of the sojourn time of the trajectory {T^k(x)}_k=0ⁿ in a small neighborhood of p to that in a small neighborhood of q. In one case the limit exists and the limit value is a constant for a.e.- x . But in the other case the limit does not exist. In fact in this case the limit supreme of the ratio is \infty and the limit infimum is 0 for a.e.- x .

We also discuss some further questions.

Date received: June 30, 1999