CHAOTIC BEHAVIOR OF HIGHER DIMENSIONAL TRANSFORMATIONS DEFINED ON COUNTABLE PARTITIONS
1993 ◽
Vol 03
(04)
◽
pp. 1045-1049
Keyword(s):
Jablonski maps are higher dimensional maps defined on rectangular partitions with each component a function of only one variable. It is well known that expanding Jablonski maps have absolutely continuous invariant measures. In this note we consider Jablonski maps defined on countable partitions. Such maps occur, for example, in multivariable number theoretic problems. The main result establishes the existence of an absolutely continuous invariant measure for Jablonski maps on a countable partition with the additional condition that the images of all the partition elements form a finite collection. An example is given.
1996 ◽
Vol 06
(06)
◽
pp. 1143-1151
1996 ◽
Vol 16
(4)
◽
pp. 735-749
◽
2009 ◽
Vol 29
(4)
◽
pp. 1185-1215
◽
1996 ◽
Vol 16
(1)
◽
pp. 1-18
◽
2008 ◽
Vol 28
(1)
◽
pp. 211-228
◽
1990 ◽
Vol 10
(4)
◽
pp. 645-656
◽
2012 ◽
Vol 396
(1)
◽
pp. 1-6
2012 ◽
Vol 33
(2)
◽
pp. 529-548
◽