<i>p</i>-adic repellers in $ {\mathbb{Q}}_{p}$ are subshifts of finite type

Aihua Fan; Lingmin Liao; Yue Fei Wang; Dan Zhou

doi:10.1016/j.crma.2006.12.007

Mathematical Analysis

p-adic repellers in

Q_{p}

are subshifts of finite type
[Les répulseurs p-adiques dans

Q_{p}

sont des sous-shifts de type fini]

Présenté par : Jean-Pierre Kahane

Aihua Fan ^1,² ; Lingmin Liao ^1,² ; Yue Fei Wang ³ ; Dan Zhou ²

¹ Department of Mathematics, Wuhan University, 430072 Wuhan, China
² LAMFA, UMR 6140 CNRS, université de Picardie, 33, rue Saint Leu, 80039 Amiens, France
³ Institute of Mathematics, AMSS, CAS, 55 East Road Zhongguancun, 100080 Beijing, China

Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 219-224.

Résumé
Abstract

Nous prouvons que tout répulseur faible transitif p-adique est isométriquement conjugué à un sous-shift de type fini où une métrique convenable est définie.

We prove that any p-adic transitive weak repeller is isometrically conjugate to a subshift of finite type where a suitable metric is defined.

Reçu le : 2006-11-21
Accepté le : 2006-12-12
Publié le : 2007-01-24

DOI : 10.1016/j.crma.2006.12.007

Affiliations des auteurs :

Aihua Fan ^{1, 2} ; Lingmin Liao ^{1, 2} ; Yue Fei Wang ³ ; Dan Zhou ²

¹ Department of Mathematics, Wuhan University, 430072 Wuhan, China
² LAMFA, UMR 6140 CNRS, université de Picardie, 33, rue Saint Leu, 80039 Amiens, France
³ Institute of Mathematics, AMSS, CAS, 55 East Road Zhongguancun, 100080 Beijing, China

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     author = {Aihua Fan and Lingmin Liao and Yue Fei Wang and Dan Zhou},
     title = {\protect\emph{p}-adic repellers in $ {\mathbb{Q}}_{p}$ are subshifts of finite type},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {219--224},
     publisher = {Elsevier},
     volume = {344},
     number = {4},
     year = {2007},
     doi = {10.1016/j.crma.2006.12.007},
     language = {en},
}

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Aihua Fan; Lingmin Liao; Yue Fei Wang; Dan Zhou. p-adic repellers in $ {\mathbb{Q}}_{p}$ are subshifts of finite type. Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 219-224. doi : 10.1016/j.crma.2006.12.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.12.007/

Bibliographie
Cité par

[1] D. Lind; B. Marcus An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, 1995

[2] W.H. Schikhof Ultrametric Calculus, Cambridge University Press, 1984

[3] C.F. Woodcock; N.P. Smart p-adic chaos and random number generation, Experiment Math., Volume 7 (1998) no. 4, pp. 333-342

Muzaffar Rahmatullaev; Akbarkhuja Tukhtabaev Some non-periodic $p$ -adic generalized Gibbs measures for the Ising model on a Cayley tree of order $k$ , Mathematical Physics, Analysis and Geometry, Volume 26 (2023) no. 3, p. 23 (Id/No 22) | DOI:10.1007/s11040-023-09465-6 | Zbl:1529.82010
Otabek Khakimov; Farrukh Mukhamedov Chaotic behavior of the $p$ -adic Potts-Bethe mapping. II, Ergodic Theory and Dynamical Systems, Volume 42 (2022) no. 11, pp. 3433-3457 | DOI:10.1017/etds.2021.96 | Zbl:1508.37027
Muzaffar Rahmatullaev; Akbarkhuja Tukhtabaev On periodic $p$ -adic generalized Gibbs measures for Ising model on a Cayley tree, Letters in Mathematical Physics, Volume 112 (2022) no. 6, p. 18 (Id/No 112) | DOI:10.1007/s11005-022-01598-z | Zbl:1508.37054
Farrukh Mukhamedov; Otabek Khakimov Chaos in $p$ -adic statistical lattice models: Potts model, Advances in non-Archimedean analysis and applications. The $p$ -adic methodology in STEAM-H, Cham: Springer, 2021, pp. 115-165 | DOI:10.1007/978-3-030-81976-7_3 | Zbl:1504.30064
Farrukh Mukhamedov; Otabek Khakimov Translation-invariant generalized $p$ -adic Gibbs measures for the Ising model on Cayley trees, Mathematical Methods in the Applied Sciences, Volume 44 (2021) no. 16, pp. 12302-12316 | DOI:10.1002/mma.7088 | Zbl:1477.82009
Jing Hua Yang; Yun Peng Xiao On dynamics of infinitely generated contractive mapping systems on $p Z_{p}$ , Acta Mathematica Sinica. English Series, Volume 36 (2020) no. 6, pp. 651-662 | DOI:10.1007/s10114-020-8451-0 | Zbl:1450.37008
姝娴万 Hausdorff Dimensions of Conformal Iterated Function Systems of Generalized Complex Continued Fractions, Pure Mathematics, Volume 10 (2020) no. 08, p. 726 | DOI:10.12677/pm.2020.108086
Mohd Ali Khameini Ahmad; Chin Hee Pah; Mansoor Saburov, PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH2018): Innovative Technologies for Mathematics Mathematics for Technological Innovation, Volume 2184 (2019), p. 020001 | DOI:10.1063/1.5136355
Jin Zhong Xu; Lan Yu Wang Topological entropy of a class of subshifts of finite type, Acta Mathematica Sinica. English Series, Volume 34 (2018) no. 12, pp. 1765-1777 | DOI:10.1007/s10114-018-7439-5 | Zbl:1407.54025
Shilei Fan; Lingmin Liao Rational map $a x + 1 / x$ on the projective line over $Q_{p}$ , Advances in ultrametric analysis. 14th international conference on $p$ -adic functional analysis, Université d'Auvergne, Aurillac, France, June 30 – July 4, 2016. Proceedings, Providence, RI: American Mathematical Society (AMS), 2018, pp. 217-230 | DOI:10.1090/conm/704/14168 | Zbl:1419.37090
Farrukh Mukhamedov; Otabek Khakimov Chaotic behavior of the $p$ -adic Potts-Bethe mapping, Discrete and Continuous Dynamical Systems, Volume 38 (2018) no. 1, pp. 231-245 | DOI:10.3934/dcds.2018011 | Zbl:1372.37022
Mohd Ali Khameini Ahmad; Lingmin Liao; Mansoor Saburov Periodic $p$ -adic Gibbs measures of $q$ -state Potts model on Cayley trees. I: The chaos implies the vastness of the set of $p$ -adic Gibbs measures, Journal of Statistical Physics, Volume 171 (2018) no. 6, pp. 1000-1034 | DOI:10.1007/s10955-018-2053-6 | Zbl:1397.82008
Shilei Fan; Lingmin Liao Rational map $a x + 1 / x$ on the projective line over $Q_{2}$ , Science China. Mathematics, Volume 61 (2018) no. 12, pp. 2221-2236 | DOI:10.1007/s11425-017-9229-3 | Zbl:1404.37121
Farrukh Mukhamedov; Hasan Akın; Mutlay Dogan On chaotic behaviour of the p-adic generalized Ising mapping and its application, Journal of Difference Equations and Applications (2017), p. 1 | DOI:10.1080/10236198.2017.1340468
Farrukh Mukhamedov; Otabek Khakimov On Julia set and chaos in $p$ -adic Ising model on the Cayley tree, Mathematical Physics, Analysis and Geometry, Volume 20 (2017) no. 4, p. 14 (Id/No 23) | DOI:10.1007/s11040-017-9254-0 | Zbl:1413.46067
Andrei Khrennikov; Ekaterina Yurova Automaton model of protein: Dynamics of conformational and functional states, Progress in Biophysics and Molecular Biology, Volume 130 (2017), p. 2 | DOI:10.1016/j.pbiomolbio.2017.02.003
Farrukh Mukhamedov; Otabek Khakimov Phase transition and chaos: $p$ -adic Potts model on a Cayley tree, Chaos, Solitons and Fractals, Volume 87 (2016), pp. 190-196 | DOI:10.1016/j.chaos.2016.04.003 | Zbl:1355.37106
Farrukh Mukhamedov; Otabek Khakimov On metric properties of unconventional limit sets of contractive non-Archimedean dynamical systems, Dynamical Systems, Volume 31 (2016) no. 4, pp. 506-524 | DOI:10.1080/14689367.2016.1158241 | Zbl:1392.37112
Joanna Furno Haar measures and Hausdorff dimensions of $p$ -adic Julia sets, Ergodic theory, dynamical systems, and the continuing influence of John C. Oxtoby. Oxtoby centennial conference, Bryn Mawr College, Bryn Mawr, PA, USA, October 30–31, 2010. Williams ergodic theory conference, Williams College, Williamstown, MA, USA, July 27–29, 2012. AMS special session on ergodic theory and symbolic dynamics, Baltimore, MD, USA, January 17–18, 2014. Proceedings, Providence, RI: American Mathematical Society (AMS), 2016, pp. 187-196 | DOI:10.1090/conm/678/13647 | Zbl:1391.37084
Farrukh Mukhamedov; Otabek Khakimov On a generalized self-similarity in the $p$ -adic field, Fractals, Volume 24 (2016) no. 4, p. 11 (Id/No 1650041) | DOI:10.1142/s0218348x16500419 | Zbl:1357.28012
F. Mukhamedov; O. Khakimov On periodic Gibbs measures of $p$ -adic Potts model on a Cayley tree, $p$ -Adic Numbers, Ultrametric Analysis, and Applications, Volume 8 (2016) no. 3, pp. 225-235 | DOI:10.1134/s2070046616030043 | Zbl:1356.82022
Farrukh Mukhamedov Renormalization method in $p$ -adic $λ$ -model on the Cayley tree, International Journal of Theoretical Physics, Volume 54 (2015) no. 10, pp. 3577-3595 | DOI:10.1007/s10773-015-2597-z | Zbl:1334.82046
Farrukh Mukhamedov; Hasan Akın On non-Archimedean recurrence equations and their applications, Journal of Mathematical Analysis and Applications, Volume 423 (2015) no. 2, pp. 1203-1218 | DOI:10.1016/j.jmaa.2014.10.046 | Zbl:1303.39011
Farrukh Mukhamedov; Mutlay Dogan On $P$ -adic $λ$ -model on the Cayley tree. II: Phase transitions, Reports on Mathematical Physics, Volume 75 (2015) no. 1, pp. 25-46 | DOI:10.1016/s0034-4877(15)60022-2 | Zbl:1321.82020
Andrei Khrennikov; Ekaterina Yurova Criteria of ergodicity for $p$ -adic dynamical systems in terms of coordinate functions, Chaos, Solitons and Fractals, Volume 60 (2014), pp. 11-30 | DOI:10.1016/j.chaos.2014.01.001 | Zbl:1348.37128
Vladimir Anashin; Andrei Khrennikov; Ekaterina Yurova Ergodicity criteria for non-expanding transformations of 2-adic spheres, Discrete and Continuous Dynamical Systems, Volume 34 (2014) no. 2, pp. 367-377 | DOI:10.3934/dcds.2014.34.367 | Zbl:1317.37115
Assis Azevedo; Maria Carvalho; António Machiavelo Dynamics of a quasi-quadratic map, Journal of Difference Equations and Applications, Volume 20 (2014) no. 1, pp. 36-48 | DOI:10.1080/10236198.2013.805754 | Zbl:1310.37048
Weiyuan Qiu; Yuefei Wang; Jinghua Yang; Yongchen Yin On metric properties of limit sets of contractive analytic non-Archimedean dynamical systems, Journal of Mathematical Analysis and Applications, Volume 414 (2014) no. 1, pp. 386-401 | DOI:10.1016/j.jmaa.2014.01.015 | Zbl:1391.37088
E. Yurova Axelsson On recent results of ergodic property for $p$ -adic dynamical systems, $p$ -Adic Numbers, Ultrametric Analysis, and Applications, Volume 6 (2014) no. 3, pp. 234-255 | DOI:10.1134/s2070046614030066 | Zbl:1347.37154
Andrei Khrennikov; Ekaterina Yurova Criteria of measure-preserving for $p$ -adic dynamical systems in terms of the van der Put basis, Journal of Number Theory, Volume 133 (2013) no. 2, pp. 484-491 | DOI:10.1016/j.jnt.2012.08.013 | Zbl:1278.37061
Farrukh Mukhamedov; Wan Nur Fairuz Alwani Wan Rozali On ap-adic Cubic Generalized Logistic Dynamical System, Journal of Physics: Conference Series, Volume 435 (2013), p. 012012 | DOI:10.1088/1742-6596/435/1/012012
Farrukh Mukhamedov On dynamical systems and phase transitions for $q + 1$ -state $p$ -adic Potts model on the Cayley tree, Mathematical Physics, Analysis and Geometry, Volume 16 (2013) no. 1, pp. 49-87 | DOI:10.1007/s11040-012-9120-z | Zbl:1280.46047
Ekaterina Yurova On measure-preserving functions over $Z_{3}$ , $p$ -Adic Numbers, Ultrametric Analysis, and Applications, Volume 4 (2012) no. 4, pp. 326-335 | DOI:10.1134/s2070046612040061 | Zbl:1291.37122
Farrukh Mukhamedov A dynamical system approach to phase transitions for $p$ -adic Potts model on the Cayley tree of order two, Reports on Mathematical Physics, Volume 70 (2012) no. 3, pp. 385-406 | DOI:10.1016/s0034-4877(12)60053-6 | Zbl:1271.82018
Aihua Fan; Lingmin Liao On minimal decomposition of $p$ -adic polynomial dynamical systems, Advances in Mathematics, Volume 228 (2011) no. 4, pp. 2116-2144 | DOI:10.1016/j.aim.2011.06.032 | Zbl:1269.37036
Vladimir S. Anashin Noncommutative algebraic dynamics: ergodic theory for profinite groups, Proceedings of the Steklov Institute of Mathematics, Volume 265 (2009), pp. 30-58 | DOI:10.1134/s0081543809020035 | Zbl:1201.37010

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