A note on the construction of nonsingular Gibbs measures

Manfred Denker; Michiko Yuri

Colloquium Mathematicae (2000)

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

Abstract

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

How to cite

top

Denker, 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. [1] J. Aaronson, An Introduction to Infinite Ergodic Theory, Amer. Math. Soc., 1997. Zbl0882.28013
  2. [2] J. Aaronson and M. Denker, Local limit theorems for Gibbs-Markov maps, preprint, Math. Gottingensis 1 (1997). 
  3. [3] J. Aaronson and M. Denker, The Poincaré series of ℂ, Ergodic Theory Dynam. Systems 19 (1999), 1-20. Zbl0920.30036
  4. [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. [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. [6] M. Denker and M. Urbański, On the existence of conformal measures, Trans. Amer. Math. Soc. 76 (1991), 193-214. Zbl0763.30008
  7. [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. [8] F. Schweiger, Ergodic Theory of Fibred Systems and Metric Number Theory, Oxford Univ. Press, Oxford, 1995. Zbl0819.11027
  9. [9] S. Tanaka, A complex continued fraction transformation and its ergodic properties, Tokyo J. Math. 8 (1985), 191-214. Zbl0581.10028
  10. [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. [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. [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. [13] M. Yuri, Thermodynamic formalism for certain nonhyperbolic maps, ibid. 19 (1999), 1365-1378. Zbl0971.37004
  14. [14] M. Yuri, Statistical properties for nonhyperbolic maps with finite range structure, Trans. Amer. Math. Soc., to appear. Zbl0981.11028

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.