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Density of fiberwise orbits in minimal iterated function systems on the circle
1. | Instituto de Matemática e Estatística, UFF, Rua Mário Santos Braga s/n - Campus Valonguinhos, Niterói, Brazil |
2. | Department of Mathematics, Shahid Beheshti University, G.C.Tehran 19839, Iran |
3. | Department of Mathematics, Ilam University, P.O. Box 69315-516, Ilam, Iran |
References:
[1] |
V. A. Antonov, Modeling Cyclic Evolution Processes: Synchronization by Means of Random Signal, Leingradskii Universitet Vestnik Matematika Mekhanika Astronomiia, 1984, 67-76. |
[2] |
A. Arbieto, A. Junqueira and B. Santiago, On weakly hyperbolic iterated functions systems,, preprint, ().
|
[3] |
M. F. Barnsley and K. Leśniak, The chaos game on a general iterated function system from a topological point of view,, preprint, ().
|
[4] |
M. F. Barnsley and A. Vince, The chaos game on a general iterated function system, Ergodic Theory and Dynam. Systems, 31 (2011), 1073-1079.
doi: 10.1017/S0143385710000428. |
[5] |
M. F. Barnsley and A. Vince, The conley attractor of an iterated function system, Bull. Aust. Math. Soc., 88 (2013), 267-279.
doi: 10.1017/S0004972713000348. |
[6] |
P. G. Barrientos and A. Raibekas, Dynamics of iterated function systems on the circle close to rotations,, to appear in Ergodic Theory and Dynam. Systems, ().
|
[7] |
C. Bonatti and N. Guelman, Smooth Conjugacy classes of circle diffeomorphisms with irrational rotation number,, preprint, ().
|
[8] |
T. Golenishcheva-Kutuzova, A. S. Gorodetski, V. Kleptsyn and D. Volk, Translation numbers define generators of $F_k^+\to Homeo_+(\mathbbS^1)$,, preprint, ().
|
[9] |
A. S. Gorodetski and Yu. S. Ilyashenko, Certain new robust properties of invariant sets and attractors of dynamical systems, Functional Analysis and Its Applications, 33 (1999), 95-105.
doi: 10.1007/BF02465190. |
[10] |
A. S. Gorodetski and Yu. S. Ilyashenko, Some properties of skew products over a horseshoe and a solenoid, Tr. Mat. Inst. Steklova, 231 (2000), 96-112. |
[11] |
A. J. Homburg, Circle diffeomorphisms forced by expanding circle maps, Ergodic Theory and Dynam. Systems, 32 (2012), 2011-2024.
doi: 10.1017/S014338571100068X. |
[12] |
A. J. Homburg, Synchronization in iterated function systems,, preprint, ().
|
[13] |
J. E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J., 30 (1981), 713-747.
doi: 10.1512/iumj.1981.30.30055. |
[14] |
V. A. Kleptsyn and M. B. Nalskii, Contraction of orbits in random dynamical systems on the circle, Functional Analysis and Its Applications, 38 (2004), 267-282.
doi: 10.1007/s10688-005-0005-9. |
show all references
References:
[1] |
V. A. Antonov, Modeling Cyclic Evolution Processes: Synchronization by Means of Random Signal, Leingradskii Universitet Vestnik Matematika Mekhanika Astronomiia, 1984, 67-76. |
[2] |
A. Arbieto, A. Junqueira and B. Santiago, On weakly hyperbolic iterated functions systems,, preprint, ().
|
[3] |
M. F. Barnsley and K. Leśniak, The chaos game on a general iterated function system from a topological point of view,, preprint, ().
|
[4] |
M. F. Barnsley and A. Vince, The chaos game on a general iterated function system, Ergodic Theory and Dynam. Systems, 31 (2011), 1073-1079.
doi: 10.1017/S0143385710000428. |
[5] |
M. F. Barnsley and A. Vince, The conley attractor of an iterated function system, Bull. Aust. Math. Soc., 88 (2013), 267-279.
doi: 10.1017/S0004972713000348. |
[6] |
P. G. Barrientos and A. Raibekas, Dynamics of iterated function systems on the circle close to rotations,, to appear in Ergodic Theory and Dynam. Systems, ().
|
[7] |
C. Bonatti and N. Guelman, Smooth Conjugacy classes of circle diffeomorphisms with irrational rotation number,, preprint, ().
|
[8] |
T. Golenishcheva-Kutuzova, A. S. Gorodetski, V. Kleptsyn and D. Volk, Translation numbers define generators of $F_k^+\to Homeo_+(\mathbbS^1)$,, preprint, ().
|
[9] |
A. S. Gorodetski and Yu. S. Ilyashenko, Certain new robust properties of invariant sets and attractors of dynamical systems, Functional Analysis and Its Applications, 33 (1999), 95-105.
doi: 10.1007/BF02465190. |
[10] |
A. S. Gorodetski and Yu. S. Ilyashenko, Some properties of skew products over a horseshoe and a solenoid, Tr. Mat. Inst. Steklova, 231 (2000), 96-112. |
[11] |
A. J. Homburg, Circle diffeomorphisms forced by expanding circle maps, Ergodic Theory and Dynam. Systems, 32 (2012), 2011-2024.
doi: 10.1017/S014338571100068X. |
[12] |
A. J. Homburg, Synchronization in iterated function systems,, preprint, ().
|
[13] |
J. E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J., 30 (1981), 713-747.
doi: 10.1512/iumj.1981.30.30055. |
[14] |
V. A. Kleptsyn and M. B. Nalskii, Contraction of orbits in random dynamical systems on the circle, Functional Analysis and Its Applications, 38 (2004), 267-282.
doi: 10.1007/s10688-005-0005-9. |
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