IMPORTANCE OF BOUNDED VARIATION CONDITION FOR STABILITY OF AN ABSOLUTELY CONTINUOUS INVARIANT MEASURE

[摘要] We give an example showing that the uniformly bounded variation condition in the compactness theorem of Gora and Boyarsky [Canad. J. Math. 41 (1989), 855 869] is crucial for L1 stability of an absolutely continuous invariant measure (acim) of a piecewise expanding transformation. The same example shows that a simple method of approximating an invariant density of a piecewise expanding transformation can give the wrong results. (C) 1994 Academic Press, Inc.

[发布日期] 1994-01-15