Abstract
Expansive rational maps T:C→ C which are not expanding with respect to the spherical metric are those which have rationally indifferent periodic points. For an atomless t-conformal measure m of such a rational map we prove the existence of a unique (up to a multiplicative constant) σ-finite, T-invariant measureμabsolutely continuous with respect to m. We also give a necessary and sufficient condition for the measureμ to be finite.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 561-580 |
| Number of pages | 20 |
| Journal | Forum Mathematicum |
| Volume | 3 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 1 1991 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics
Cite this
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Absolutely Continuous Invariant Measures for Expansive Rational Maps with Rationally Indifferent Periodic Points. / Denker, Manfred Heinz; Urbanski, Mariusz.
In: Forum Mathematicum, Vol. 3, No. 3, 01.01.1991, p. 561-580.Research output: Contribution to journal › Article
TY - JOUR
T1 - Absolutely Continuous Invariant Measures for Expansive Rational Maps with Rationally Indifferent Periodic Points
AU - Denker, Manfred Heinz
AU - Urbanski, Mariusz
PY - 1991/1/1
Y1 - 1991/1/1
N2 - Expansive rational maps T:C→ C which are not expanding with respect to the spherical metric are those which have rationally indifferent periodic points. For an atomless t-conformal measure m of such a rational map we prove the existence of a unique (up to a multiplicative constant) σ-finite, T-invariant measureμabsolutely continuous with respect to m. We also give a necessary and sufficient condition for the measureμ to be finite.
AB - Expansive rational maps T:C→ C which are not expanding with respect to the spherical metric are those which have rationally indifferent periodic points. For an atomless t-conformal measure m of such a rational map we prove the existence of a unique (up to a multiplicative constant) σ-finite, T-invariant measureμabsolutely continuous with respect to m. We also give a necessary and sufficient condition for the measureμ to be finite.
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UR - http://www.scopus.com/inward/citedby.url?scp=0039123326&partnerID=8YFLogxK
U2 - 10.1515/form.1991.3.561
DO - 10.1515/form.1991.3.561
M3 - Article
AN - SCOPUS:0039123326
VL - 3
SP - 561
EP - 580
JO - Forum Mathematicum
JF - Forum Mathematicum
SN - 0933-7741
IS - 3
ER -