# A note on the construction of nonsingular Gibbs measures

Colloquium Mathematicae (2000)

- Volume: 84/85, Issue: 2, page 377-383
- ISSN: 0010-1354

## Access Full Article

top## Abstract

top## How to cite

topDenker, Manfred, and Yuri, Michiko. "A note on the construction of nonsingular Gibbs measures." Colloquium Mathematicae 84/85.2 (2000): 377-383. <http://eudml.org/doc/210820>.

@article{Denker2000,

abstract = {We give a sufficient condition for the construction of Markov fibred systems using countable Markov partitions with locally bounded distortion.},

author = {Denker, Manfred, Yuri, Michiko},

journal = {Colloquium Mathematicae},

keywords = {Perron-Frobenius operator; Markov partition; Gibbs measure; Schweiger property},

language = {eng},

number = {2},

pages = {377-383},

title = {A note on the construction of nonsingular Gibbs measures},

url = {http://eudml.org/doc/210820},

volume = {84/85},

year = {2000},

}

TY - JOUR

AU - Denker, Manfred

AU - Yuri, Michiko

TI - A note on the construction of nonsingular Gibbs measures

JO - Colloquium Mathematicae

PY - 2000

VL - 84/85

IS - 2

SP - 377

EP - 383

AB - We give a sufficient condition for the construction of Markov fibred systems using countable Markov partitions with locally bounded distortion.

LA - eng

KW - Perron-Frobenius operator; Markov partition; Gibbs measure; Schweiger property

UR - http://eudml.org/doc/210820

ER -

## References

top- [1] J. Aaronson, An Introduction to Infinite Ergodic Theory, Amer. Math. Soc., 1997. Zbl0882.28013
- [2] J. Aaronson and M. Denker, Local limit theorems for Gibbs-Markov maps, preprint, Math. Gottingensis 1 (1997).
- [3] J. Aaronson and M. Denker, The Poincaré series of ℂ, Ergodic Theory Dynam. Systems 19 (1999), 1-20. Zbl0920.30036
- [4] J. Aaronson, M. Denker and M. Urbański, Ergodic theory for Markov fibred systems and parabolic rational maps, Trans. Amer. Math. Soc. 337 (1993), 495-548. Zbl0789.28010
- [5] M. Denker and M. Urbański, Absolutely continuous invariant measures for expansive rational maps with rationally indifferent periodic points, Forum Math. 3 (1991), 561-579. Zbl0745.28008
- [6] M. Denker and M. Urbański, On the existence of conformal measures, Trans. Amer. Math. Soc. 76 (1991), 193-214. Zbl0763.30008
- [7] P. Hanus, R. D. Mauldin and M. Urbański, Thermodynamic formalism and multi-fractal analysis of conformal infinite iterated functional systems, preprint, IHES, 1999. Zbl1012.28007
- [8] F. Schweiger, Ergodic Theory of Fibred Systems and Metric Number Theory, Oxford Univ. Press, Oxford, 1995. Zbl0819.11027
- [9] S. Tanaka, A complex continued fraction transformation and its ergodic properties, Tokyo J. Math. 8 (1985), 191-214. Zbl0581.10028
- [10] P. Walters, Invariant measures and equilibrium states for some mappings which expand distances, Trans. Amer. Math. Soc. 236 (1978), 121-153. Zbl0375.28009
- [11] M. Yuri, On a Bernoulli property for multi-dimensional mappings with finite range structure, Tokyo J. Math. 9 (1986), 457-485. Zbl0625.58001
- [12] M. Yuri, On the convergence to equilibrium states for certain non-hyperbolic systems, Ergodic Theory Dynam. Systems 17 (1997), 977-1000. Zbl0887.58033
- [13] M. Yuri, Thermodynamic formalism for certain nonhyperbolic maps, ibid. 19 (1999), 1365-1378. Zbl0971.37004
- [14] M. Yuri, Statistical properties for nonhyperbolic maps with finite range structure, Trans. Amer. Math. Soc., to appear. Zbl0981.11028

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.