Advanced search
Publication Cover
Experimental Mathematics Volume 7, 1998 - Issue 4
Submit an article Journal homepage
62
Views
44
CrossRef citations to date
0
Altmetric
Original Articles

p-adic Chaos and Random Number Generation

Christopher F. Woodcock Institute of Mathematics and Statistics, University of Kent, Canterbury, Kent, CT2 7NF, United Kingdom E-mail: [email protected]
&
Nigel P. Smart Hewlett-Packard Laboratories, FUton Road, Stoke Gifford, Bristol, BS12 6QZ, United Kingdom E-mail: [email protected]
Pages 333-342 | Published online: 03 Apr 2012

Citations (44)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (3)

Farrukh Mukhamedov, Hasan Akın & Mutlay Dogan. (2017) On chaotic behaviour of the p-adic generalized Ising mapping and its application. Journal of Difference Equations and Applications 23:9, pages 1542-1561.
Read now
U.V. Chetana & B.R. Shankar. (2017) Chaotic dynamical systems on symbolic spaces. Journal of Dynamical Systems and Geometric Theories 15:2, pages 131-146.
Read now
Farrukh Mukhamedov & Otabek Khakimov. (2016) On metric properties of unconventional limit sets of contractive non-Archimedean dynamical systems. Dynamical Systems 31:4, pages 506-524.
Read now

Articles from other publishers (41)

Muzaffar Rahmatullaev & Akbarkhuja Tukhtabaev. (2023) Some Non-periodic p-Adic Generalized Gibbs Measures for the Ising Model on a Cayley Tree of Order k. Mathematical Physics, Analysis and Geometry 26:3.
Crossref
Muzaffar Rahmatullaev & Akbarkhuja Tukhtabaev. (2022) On periodic p-adic generalized Gibbs measures for Ising model on a Cayley tree. Letters in Mathematical Physics 112:6.
Crossref
OTABEK KHAKIMOV & FARRUKH MUKHAMEDOV. (2021) Chaotic behavior of the p -adic Potts–Bethe mapping II . Ergodic Theory and Dynamical Systems 42:11, pages 3433-3457.
Crossref
Jonte R. Hance, Sabine Hossenfelder & Tim N. Palmer. (2022) Supermeasured: Violating Bell-Statistical Independence Without Violating Physical Statistical Independence. Foundations of Physics 52:4.
Crossref
Farrukh Mukhamedov & Otabek Khakimov. (2020) Translation‐invariant generalized P ‐adic Gibbs measures for the Ising model on Cayley trees . Mathematical Methods in the Applied Sciences 44:16, pages 12302-12316.
Crossref
Jéfferson L.R. Bastos, Danilo A. Caprio & Ali Messaoudi. (2021) Shadowing and stability in p-adic dynamics. Journal of Mathematical Analysis and Applications 500:2, pages 125117.
Crossref
CLAYTON PETSCHE. (2020) Attractors associated to a family of hyperbolic -adic plane automorphisms. Ergodic Theory and Dynamical Systems 41:6, pages 1867-1882.
Crossref
Farrukh Mukhamedov & Otabek Khakimov. 2021. Advances in Non-Archimedean Analysis and Applications. Advances in Non-Archimedean Analysis and Applications 115 165 .
T. N. Palmer. 2021. Undecidability, Uncomputability, and Unpredictability. Undecidability, Uncomputability, and Unpredictability 81 95 .
Yûsuke Okuyama & Małgorzata Stawiska. (2020) On a Characterization of Polynomials Among Rational Functions in Non-Archimedean Dynamics. Arnold Mathematical Journal 6:3-4, pages 407-430.
Crossref
T. N. Palmer. (2020) Discretization of the Bloch sphere, fractal invariant sets and Bell’s theorem. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476:2236.
Crossref
Joanna Furno. (2019) Natural extensions for -adic -shifts and other scaling maps . Indagationes Mathematicae 30:6, pages 1099-1108.
Crossref
V. P. Kharchenko & N. M. Glazunov. (2019) Formal and Non-Archimedean Structures of Dynamic Systems on Manifolds. Cybernetics and Systems Analysis 55:3, pages 384-392.
Crossref
Sangtae Jeong. (2018) Bernoulli maps on Z in the expansions of van der Put and Mahler. Journal of Number Theory 193, pages 235-265.
Crossref
Shilei Fan & Lingmin Liao. (2018) Rational map ax + 1/x on the projective line over ℚ2. Science China Mathematics 61:12, pages 2221-2236.
Crossref
Kenneth Allen, David DeMark & Clayton Petsche. (2018) Non-Archimedean Hénon maps, attractors, and horseshoes. Research in Number Theory 4:1.
Crossref
Farrukh Mukhamedov & Otabek Khakimov. (2017) On Julia Set and Chaos in p-adic Ising Model on the Cayley Tree. Mathematical Physics, Analysis and Geometry 20:4.
Crossref
Farrukh Mukhamedov & Otabek Khakimov. (2017) Chaotic behavior of the $P$-adic Potts-Bethe mapping. Discrete and Continuous Dynamical Systems 38:1, pages 231-245.
Crossref
FARRUKH MUKHAMEDOV & OTABEK KHAKIMOV. (2016) ON A GENERALIZED SELF-SIMILARITY IN THE p-ADIC FIELD. Fractals 24:04, pages 1650041.
Crossref
Farrukh Mukhamedov & Otabek Khakimov. (2016) Phase transition and chaos: P -adic Potts model on a Cayley tree. Chaos, Solitons & Fractals 87, pages 190-196.
Crossref
Franco Vivaldi. (2016) Discrete resonances. Modern Physics Letters B 29:35n36, pages 1530016.
Crossref
Farrukh Mukhamedov. (2015) Renormalization Method in p-Adic ?-Model on the Cayley Tree. International Journal of Theoretical Physics 54:10, pages 3577-3595.
Crossref
Farrukh Mukhamedov. (2014) On the strong phase transition for the one-dimensional countable state p -adic Potts model . Journal of Statistical Mechanics: Theory and Experiment 2014:1, pages P01007.
Crossref
Farrukh Mukhamedov & Wan Nur Fairuz Alwani Wan Rozali. (2013) On a p -adic Cubic Generalized Logistic Dynamical System . Journal of Physics: Conference Series 435, pages 012012.
Crossref
Farrukh Mukhamedov. (2012) On Dynamical Systems and Phase Transitions for q?+?1-state p-adic Potts Model on the Cayley Tree. Mathematical Physics, Analysis and Geometry 16:1, pages 49-87.
Crossref
Farrukh Mukhamedov. (2012) A Dynamical System Approach to Phase Transitions for p-Adic Potts Model on the Cayley Tree of Order Two. Reports on Mathematical Physics 70:3, pages 385-406.
Crossref
Aihua Fan & Lingmin Liao. (2011) On minimal decomposition of p-adic polynomial dynamical systems. Advances in Mathematics 228:4, pages 2116-2144.
Crossref
James Kingsbery, Alex Levin, Anatoly Preygel & Cesar Silva. (2011) Dynamics of the $p$-adic shift and applications. Discrete and Continuous Dynamical Systems 30:1, pages 209-218.
Crossref
Alina Ostafe & Igor E. Shparlinski. (2011) Pseudorandomness and Dynamics of Fermat Quotients. SIAM Journal on Discrete Mathematics 25:1, pages 50-71.
Crossref
Karl-Olof Lindahl. (2010) Applied algebraic dynamics. P-Adic Numbers, Ultrametric Analysis, and Applications 2:4, pages 360-362.
Crossref
Abdelaziz Bellagh. (2010) SEMIGROUP OF RATIONAL $p$-ADIC FUNCTIONS FOR COMPOSITION. Taiwanese Journal of Mathematics 14:4.
Crossref
Madhekar Suneel. (2009) Cryptographic pseudo-random sequences from the chaotic H?non map. Sadhana 34:5, pages 689-701.
Crossref
Fuyan Sun & Shutang Liu. (2009) Cryptographic pseudo-random sequence from the spatial chaotic map. Chaos, Solitons & Fractals 41:5, pages 2216-2219.
Crossref
Aihua Fan, Lingmin Liao, Yue Fei Wang & Dan Zhou. (2007) p-adic repellers in are subshifts of finite type. Comptes Rendus Mathematique 344:4, pages 219-224.
Crossref
Farrukh Mukhamedov & José F. F. Mendes. 2008. Differential Equations, Chaos and Variational Problems. Differential Equations, Chaos and Variational Problems 305 315 .
N. Masuda, G. Jakimoski, K. Aihara & L. Kocarev. (2006) Chaotic block ciphers: from theory to practical algorithms. IEEE Transactions on Circuits and Systems I: Regular Papers 53:6, pages 1341-1352.
Crossref
Ping Li, Zhong Li, Wolfgang A. Halang & Guanrong Chen. (2006) A multiple pseudorandom-bit generator based on a spatiotemporal chaotic map. Physics Letters A 349:6, pages 467-473.
Crossref
FRANCO VIVALDI & IGOR VLADIMIROV. (2011) PSEUDO-RANDOMNESS OF ROUND-OFF ERRORS IN DISCRETIZED LINEAR MAPS ON THE PLANE. International Journal of Bifurcation and Chaos 13:11, pages 3373-3393.
Crossref
J. Pettigrew, J. A. G. Roberts & F. Vivaldi. (2001) Complexity of regular invertible p -adic motions . Chaos: An Interdisciplinary Journal of Nonlinear Science 11:4, pages 849-857.
Crossref
Andrei Khrennikov. (2001) Small denominators in complex p-adic dynamics. Indagationes Mathematicae 12:2, pages 177-189.
Crossref
D Bosio & F Vivaldi. (2000) Round-off errors and p -adic numbers . Nonlinearity 13:1, pages 309-322.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.