Absolutely continuous invariant measures for piecewise expanding C2 transformations in Rn on domains with cusps on the boundaries
1996 ◽
Vol 16
(1)
◽
pp. 1-18
◽
Keyword(s):
AbstractLet Ω be a bounded region in Rn and let be a partition of Ω into a finite number of subsets having piecewise C2 boundaries. The boundaries may contain cusps. Let τ: Ω → Ω be piecewise C2 on and expanding in the sense that there exists α > 1 such that for any i = 1, 2,…,m, where is the derivative matrix of and ‖·‖ is the euclidean matrix norm. The main result provides a lower bound on α which guarantees the existence of an absolutely continuous invariant measure for τ.
1993 ◽
Vol 03
(04)
◽
pp. 1045-1049
1996 ◽
Vol 06
(06)
◽
pp. 1143-1151
1996 ◽
Vol 16
(4)
◽
pp. 735-749
◽
2009 ◽
Vol 29
(4)
◽
pp. 1185-1215
◽
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
◽