A note on the construction of nonsingular Gibbs measures
Denker, Manfred ; Yuri, Michiko
Colloquium Mathematicae, Tome 84/85 (2000), p. 377-383 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:210820 
@article{bwmeta1.element.bwnjournal-article-cmv84i2p377bwm,
     author = {Manfred Denker and Michiko Yuri},
     title = {A note on the construction of nonsingular Gibbs measures},
     journal = {Colloquium Mathematicae},
     volume = {84/85},
     year = {2000},
     pages = {377-383},
     zbl = {0960.37003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv84i2p377bwm}
}

Denker, Manfred; Yuri, Michiko. A note on the construction of nonsingular Gibbs measures. Colloquium Mathematicae, Tome 84/85 (2000) pp. 377-383. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv84i2p377bwm/

[000] [1] J. Aaronson, An Introduction to Infinite Ergodic Theory, Amer. Math. Soc., 1997. | Zbl 0882.28013

[001] [2] J. Aaronson and M. Denker, Local limit theorems for Gibbs-Markov maps, preprint, Math. Gottingensis 1 (1997).

[002] [3] J. Aaronson and M. Denker, The Poincaré series of ℂ, Ergodic Theory Dynam. Systems 19 (1999), 1-20. | Zbl 0920.30036

[003] [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. | Zbl 0789.28010

[004] [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. | Zbl 0745.28008

[005] [6] M. Denker and M. Urbański, On the existence of conformal measures, Trans. Amer. Math. Soc. 76 (1991), 193-214. | Zbl 0763.30008

[006] [7] P. Hanus, R. D. Mauldin and M. Urbański, Thermodynamic formalism and multi-fractal analysis of conformal infinite iterated functional systems, preprint, IHES, 1999. | Zbl 1012.28007

[007] [8] F. Schweiger, Ergodic Theory of Fibred Systems and Metric Number Theory, Oxford Univ. Press, Oxford, 1995. | Zbl 0819.11027

[008] [9] S. Tanaka, A complex continued fraction transformation and its ergodic properties, Tokyo J. Math. 8 (1985), 191-214. | Zbl 0581.10028

[009] [10] P. Walters, Invariant measures and equilibrium states for some mappings which expand distances, Trans. Amer. Math. Soc. 236 (1978), 121-153. | Zbl 0375.28009

[010] [11] M. Yuri, On a Bernoulli property for multi-dimensional mappings with finite range structure, Tokyo J. Math. 9 (1986), 457-485. | Zbl 0625.58001

[011] [12] M. Yuri, On the convergence to equilibrium states for certain non-hyperbolic systems, Ergodic Theory Dynam. Systems 17 (1997), 977-1000. | Zbl 0887.58033

[012] [13] M. Yuri, Thermodynamic formalism for certain nonhyperbolic maps, ibid. 19 (1999), 1365-1378. | Zbl 0971.37004

[013] [14] M. Yuri, Statistical properties for nonhyperbolic maps with finite range structure, Trans. Amer. Math. Soc., to appear. | Zbl 0981.11028