Show Summary Details
More options …

# Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
ISSN
1572-9176
See all formats and pricing
More options …

# Accessibility on iterated function systems

Maliheh Mohtashamipour
Published Online: 2019-06-13 | DOI: https://doi.org/10.1515/gmj-2019-2032

## Abstract

In this paper, we define accessibility on an iterated function system (IFS) and show that it provides a sufficient condition for the transitivity of this system and its corresponding skew product. Then, by means of a certain tool, we obtain the topologically mixing property. We also give some results about the ergodicity and stability of accessibility and, further, illustrate accessibility by some examples.

MSC 2010: 37B05; 54H20

## References

• [1]

A. Z. Bahabadi, Shadowing and average shadowing properties for iterated function systems, Georgian Math. J. 22 (2015), no. 2, 179–184.

• [2]

P. G. Barrientos, A. Fakhari, D. Malicet and A. Sarizadeh, Expanding actions: Minimality and ergodicity, Stoch. Dyn. 17 (2017), no. 4, Article ID 1750031.

• [3]

M. I. Brin and J. B. Pesin, Partially hyperbolic dynamical systems (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 170–212; translation in Math. USSR-Izv. 8 (1974), no. 1, 177–218. Google Scholar

• [4]

K. Burns, D. Dolgopyat and Y. Pesin, Partial hyperbolicity, Lyapunov exponents and stable ergodicity, J. Statist. Phys. 108 (2002), no. 5–6, 927–942.

• [5]

K. Burns, F. R. Hertz, M. A. R. Hertz, A. Talitskaya and R. Ures, Density of accessibility for partially hyperbolic diffeomorphisms with one-dimensional center, Discrete Contin. Dyn. Syst. 22 (2008), no. 1–2, 75–88.

• [6]

K. Burns, C. Pugh and A. Wilkinson, Stable ergodicity and Anosov flows, Topology 39 (2000), no. 1, 149–159.

• [7]

P. Didier, Stability of accessibility, Ergodic Theory Dynam. Systems 23 (2003), no. 6, 1717–1731.

• [8]

D. Dolgopyat and A. Wilkinson, Stable accessibility is ${C}^{1}$ dense, Geometric Methods in Dynamics. II, Astérisque 287, Société Mathématique de France, Paris (2003), 33–60. Google Scholar

• [9]

M. Fatehi Nia and S. A. Ahmadi, Various shadowing properties for parameterized iterated function systems, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 80 (2018), no. 1, 145–154. Google Scholar

• [10]

A. J. Homburg and M. Nassiri, Robust minimality of iterated function systems with two generators, Ergodic Theory Dynam. Systems 34 (2014), no. 6, 1914–1929.

• [11]

A. Koropecki and M. Nassiri, Transitivity of generic semigroups of area-preserving surface diffeomorphisms, Math. Z. 266 (2010), no. 3, 707–718.

• [12]

M. Mohtashamipour and A. Z. Bahabadi, Two-sided limit shadowing property on iterated function systems, Kragujevac J. Math. 44 (2020), no. 1, 113–125. Google Scholar

• [13]

J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286–294.

• [14]

V. Niţică and A. Török, An open dense set of stably ergodic diffeomorphisms in a neighborhood of a non-ergodic one, Topology 40 (2001), no. 2, 259–278.

• [15]

J. F. Plante, Anosov flows, Amer. J. Math. 94 (1972), 729–754.

• [16]

C. Pugh and M. Shub, Stably ergodic dynamical systems and partial hyperbolicity, J. Complexity 13 (1997), no. 1, 125–179.

• [17]

C. Pugh and M. Shub, Stable ergodicity and julienne quasi-conformality, J. Eur. Math. Soc. (JEMS) 2 (2000), no. 1, 1–52.

• [18]

F. B. Rodrigues and P. Varandas, Specification and thermodynamical properties of semigroup actions, J. Math. Phys. 57 (2016), no. 5, Article ID 052704.

• [19]

F. Rodriguez Hertz, Stable ergodicity of certain linear automorphisms of the torus, Ann. of Math. (2) 162 (2005), no. 1, 65–107.

• [20]

R. Sacksteder, Strongly mixing transformations, Global Analysis, Proc. Sympos. Pure Math. 14, American Mathematical Society, Providence (1970), 245–252. Google Scholar

• [21]

M. Shub and A. Wilkinson, Stably ergodic approximation: Two examples, Ergodic Theory Dynam. Systems 20 (2000), no. 3, 875–893.

Revised: 2018-04-15

Accepted: 2018-04-23

Published Online: 2019-06-13

Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X,

Export Citation

© 2019 Walter de Gruyter GmbH, Berlin/Boston.