Teorema. uchun quyidagicha bo’ladi:
Foydalanilgan adabiyotlar
Devaney R.L. An introduction to chaotic dynamical systems,Westview Press,2003.
Roziqov U.A. An introduction to mathematical billiards.World Sci.Publ.Singapore,2019,224 bet.
Roziqov U.A,Sattorov I.A. Dynamical systems of the p-adic rational functions with two fixed points.Result in mathematics, 2020.V.75., No.3, Paper No.100, 37 pp.
Roziqov U.A. Population dynamics:algebraic and probabilistic approach.World Sci.Publ.Singapore. 2020, 460 bet.
Robinson.R.L . An introduction to dynamical system, continuous and discrete. Pearson Educ.Inc.2004.
Elaydi.S.N. Discrete chaos.Chapman Hall/CRC.2000.
Gʻanixodjayev R.N. “Квадратичный стохастические операторы” Докторc.Дисс.1992.
Ganikhodzhaev R.N, Mukhamedov F.M, Roziqov U.A. Quadratic stochastic operators and processes: result and open problems. Inf.Dim.Anal.Quant.Prob.Rel.Fields. 2011.V.14,No.2,p.279-335.
Galor O. Discrete dynamical systems. Springer -Berlin-2007,153 p.
Katok A, Hasselblatt B. Introduction to the modern theory of dynamical systems// Encyclopedia of mathematics and its applications- Cambridge Univ.Press-London, 2005-V.54-802p.
Sharkovskii A.N and etc.The dynamics of one-dimensional maps. Mathematics and its applications. V.407. Springer Netherlands-1997, 262p.
Murray J.D. Mathematical Biology: An Introduction. Springer-Verlag, Berlin.
Benedetto R. Hyperbolic maps in p-adic dynamics. Ergodic Theory and Dynamical Systems. 21 (2001), p. 1-11.
Benedetto R. p-Adic dynamics and Sullivanʻs no wandering domains theorem. Compositio Mathematics. 122 (2000), p. 281-298.
Call G. and Silverman J. Canonical height on varieties with morphisms. Compositio Mathematics. 89 (1993), p. 163-205.
Dubischer D., Gundlach V.M., Khrennikov A. and Steinkamp O. Attractors of random dynamical system over p-adic numbers and a model of “noisy” cognitive process. Physica D. 130 (1999), p. 1-12.
Fan A.H. and Liao L.M. On minimal decomposition of p-adic polynomial dynamical systems . Advances in Mathematics. 228 (2011), p. 2116–2144.
Fan A., Fan S., Liao L., Wang Y. On minimal decomposition of p-adic homographic dynamical systems. Advances in Mathematics. 257 (2014),
p. 92–135.
Ganikhodjaev N.N., Mukhamedov F.M. and Rozikov U.A. Existence of phase transition for the Potts p-adic model on the set Zp . Theoretical and Mathematical Physics. 130 (2002), p. 425-431.
Gandolfo D., Rozikov U.A., Ruiz J. On p-adic Gibbs Measures for Hard Core Model on a Cayley Tree . Markov Process. Related Fields 18 (4), (2012), p. 701–720.
Gouvea F.Q. p-Adic Numbers: An Introduction. Springer-Verlag, Berlin Heidelberg, New York, second edition, 1997.
Sattarov I.A. p-Adic (3,2)–rational dynamical systems with three fixed points. Uzbek Mathematical Journal. 2019. N. 3, p.85-100.
Schikhof W.H. Ultrametric calculus. An introduction to p-adic analysis. Cambridge University Press, Cambridge, 1984.
Svensson P.-A. Two-periodic dynamics in finite extensions of the p-adic number field. Proc. Steklov Inst. Math. 265(1) (2009), p. 235-241.
Thiran E., Verstegen D. and Weters J. p-adic dynamics. Journal of Statistical Physics. 54(3/4) (1989), p. 893-913.
Vladimirov V.S., Volovich I.V. and Zelenov E.I., p-adic Analysis and Mathematical Physics. World Scientific, Singapore, 1994.
Yoccoz J.-C. and Herman M. Generalizations of some theorems of small divisors tp non-Archimedean fields. In: Geometric Dynamics (Rio de Janeiro, 1981), Lec. Notes in Math. 1007, Springer, Berlin, 1983, p. 408-447.
A.R. Luna, U.A. Rozikov, I.A. Sattarov. P-adik dynamical systems of (3,1)-rational functions with unique fixed point. Arxiv:1807.11561v2 [math. DS] 2018.
U.A. Rozikov. p-adik dynamical systems of the rational function . Arxiv: 2101.05750v1 [math. DS] 2021.
U.A. Rozikov. What are p-adic numbers? What are they used for? Asia Pac. Math. Newsl. 3(4)(2013), 1-6.
Do'stlaringiz bilan baham: |