On the convergence to equilibrium states for certain non-hyperbolic systems
MICHIKO YURI a1 a1 Department of Business Administration,
Sapporo University, Nishioka, Toyohira-ku, Sapporo 062,
We study the convergence to equilibrium states for
certain non-hyperbolic piecewise invertible systems.
The multi-dimensional maps we shall consider
do not satisfy Renyi's condition (uniformly
bounded distortion for any iterates) and do not necessarily
satisfy the Markov property.
The failure of both conditions may cause singularities of
densities of the invariant measures, even if they are
finite, and causes a crucial difficulty in applying the
standard technique of the Perron–Frobenius
operator. Typical examples of maps we consider
admit indifferent periodic orbits and arise in many contexts.
For the convergence of iterates of
the Perron–Frobenius operator,
we study continuity of the invariant density.