Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (2): 305-320.
Xufei Lu1(),Changhua Jiao2(
),Jinghua Yang1,*(
)
Received:
2023-11-23
Revised:
2024-10-15
Online:
2025-04-26
Published:
2025-04-09
Contact:
Jinghua Yang
E-mail:luxufei@shu.edu.cn;jch23@mails.tsinghua.edu.cn;jhyang@shu.edu.cn
Supported by:
CLC Number:
Xufei Lu,Changhua Jiao,Jinghua Yang. Affine Semigroup Dynamical Systems on Zp[J].Acta mathematica scientia,Series A, 2025, 45(2): 305-320.
[1] | Anashin V, Khrennikov A. Applied Algebraic Dynamics. New York: Walter de Gruyter, 2009 |
[2] | Baker M, Rumely R S. Potential Theory and Dynamics on the Berkovich Projective Line. Providence: American Mathematical Society, 2010 |
[3] | Khrennikov A Y. Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models. Dordrecht: Kluwer Academic Publishers, 1997 |
[4] | Khrennikov A Y, Nilson M. p-Adic Deterministic and Random Dynamics. Berlin:Springer Nature, 2013 |
[5] | Silverman J H. The Arithmetic of Dynamical Systems. New York: Springer-Verlag, 2007 |
[6] | Ahmadi O, Luca F, Ostafe A, Shparlinski I E. On stable quadratic polynomials. Glasgow Mathematical Journal, 2012, 54(2): 359-369 |
[7] | Albeverio S, Gundlach M, Khrennikov A, Lindahl K O. On Markovian behaviour of p-adic random dynamical systems. Journal of Mathematical Physics, 2004, 8(2): 135-152 |
[8] | Amerik E. Existence of non-preperiodic algebraic points for a rational self-map of infinite order. Mathematical Research Letters, 2011, 18(2): 251-256 |
[9] | Anashin V. Ergodic transformations in the space of p-adic integers. American Institute of Physics, 2006, 826(1): 3-24. |
[10] | Oxtoby J C. Ergodic sets. Bulletin of the American Mathematical Society, 1952, 58(2): 116-136 |
[11] | Fan A H, Li M T, Yao J Y, et al. p-adic affine dynamical systems and applications. Comptes Rendus Mathematique, 2006, 342(2): 129-134 |
[12] | Fan A, Liao L. On minimal decomposition of p-adic polynomial dynamical systems. Advances in Mathematics, 2011, 228(4): 2116-2144 |
[13] | Fan A H, Li M T, Yao J Y, et al. Strict ergodicity of affine p-adic dynamical systems on Zp. Advances in Mathematics, 2007, 214(2): 666-700 |
[14] | Fan A, Fan S, Liao L, et al. On minimal decomposition of p-adic homographic dynamical systems. Advances in Mathematics, 2014, 257: 92-135 |
[15] | Durand F, Paccaut F. Minimal polynomial dynamics on the set of 3-adic integers. Bulletin of the London Mathematical Society, 2009, 41(2): 302-314 |
[16] | Fan S L, Liao L M. Dynamical structures of Chebyshev polynomials on Z2. Journal of Number Theory, 2016, 169: 174-182 |
[17] | Fan S L, Liao L M. Dynamics of the square mapping on the ring of p-adic integers. Proceedings of the American Mathematical Society, 2016, 144(3): 1183-1196 |
[18] | Jung M, Kim D. Dynamic structures of p-adic monomials for small primes p. Journal of Number Theory, 2020, 211: 155-183 |
[19] | Kim D, Kwon Y, Song K. Minimality of 5-adic polynomial dynamical systems. Dynamical Systems, 2020, 35(4): 584-596 |
[20] | Jeong S. Ergodic functions over Zp. Journal of Number Theory, 2022, 232: 423-479 |
[21] | Khrennikov A. p-adic discrete dynamical systems and collective behaviour of information states in cognitive models. Discrete Dynamics in Nature and Society, 2000, 5: 59-69 |
[22] | Bézivin J P. Sur la compacité des ensembles de Julia des polynmes p-adiques. Mathematische Zeitschrift, 2004, 246(1/2): 273-289 |
[23] | Fan A, Liao L, Wang Y F, et al. p-adic repellers in Qp are subshifts of finite type. Comptes Rendus Mathematique, 2007, 344(4): 219-224 |
[24] | Khrennikov A Y. p-adic dynamical systems: description of concurrent struggle in a biological population with limited growth. Doklady Akademii Nauk, 1998, 361(6): 752-754 |
[25] | Qiu W Y, Yang J H, Yin Y C. The discrete subgroups and Jørgensen's inequality for SL(m,Cp). Acta Mathematica Sinica-English Series, 2013, 29(3): 417-428 |
[26] | Qiu W Y, Wang Y F, Yang J H, Yin Y C. On metric properties of limit sets of contractive analytic non-Archimedean dynamical systems. J Math Anal Appl, 2014, 414(1): 386-401 |
[27] | Rivera-Letelier J. Espace hyperbolique p-adique et dynamique des fonctions rationnelles. Compositio Mathematica, 2003, 138(2): 199-231 |
[28] | Rivera-Letelier J. Points périodiques des fonctions rationnelles dans l'espace hyperbolique p-adique. Commentarii Mathematici Helvetici, 2005, 80(3): 593-629 |
[29] | Wang Y F, Yang J H. The pointwise convergence of p-adic {M}öbius maps. Science China-mathematics, 2014, 57(1): 1-8 |
[30] | Yang J H. On the discrete criteria and Jørgensen inequalities for SL(m,¯F((t))). Chineses Annals of Mathematics, 2019, 40(2): 227-236 |
[31] | Yang J H, Xiao Y P. On dynamics of infinitely generated contractive mapping systems on pZp. Acta Mathematica Sinica-English Series, 2020, 36(6): 651-662 |
[1] | Lin Li,Lingling Liu,Zhiheng Yu. On Classification of Planar Cubic Polynomials [J]. Acta mathematica scientia,Series A, 2025, 45(2): 554-566. |
[2] | Yanxue Lin. Dynamical Localization for the CMV Matrices with Verblunsky Coeffcients Defined by the Skew-Shift [J]. Acta mathematica scientia,Series A, 2025, 45(2): 334-346. |
[3] | Zhang Yiran, Li Dingshi. Invariant Measure of Impulsive Fractional Lattice System [J]. Acta mathematica scientia,Series A, 2024, 44(6): 1563-1576. |
[4] | Lian Yuan, Liu Hongjun, Zhu Bin. Weyl Mean Equicontinuity and Weyl Mean Sensitivity of A Random Dynamical System [J]. Acta mathematica scientia,Series A, 2024, 44(6): 1595-1606. |
[5] | Xiao Jianrong. Robust Accessible Hyperbolic Repelling Sets [J]. Acta mathematica scientia,Series A, 2024, 44(1): 1-11. |
[6] | Fu Qinhong, Xiong Lianglin, Zhang Haiyang, Qin Ya, Quan Shenai. Sliding Mode Control for Time-Varying Delay Systems with Semi-Markov Jump [J]. Acta mathematica scientia,Series A, 2023, 43(2): 549-562. |
[7] |
Zhu Kaixuan, Sun Tao, Xie Yongqin.
Global Attractors for a Class of Reaction-Diffusion Equations with Distribution Derivatives in |
[8] | Kaixuan Zhu,Yongqin Xie,Xinyu Mei,Xijun Deng. Uniform Attractors for the Sup-Cubic Weakly Damped Wave Equations with Delays [J]. Acta mathematica scientia,Series A, 2022, 42(1): 86-102. |
[9] | Yue Sun,Daoxiang Zhang,Wen Zhou. The Influence of Fear Effect on Stability Interval of Reaction-Diffusion Predator-Prey System with Time Delay [J]. Acta mathematica scientia,Series A, 2021, 41(6): 1980-1992. |
[10] | Xiaofang Yang,Xiao Tang,Tianxiu Lu. The Collectively Sensitivity and Accessible in Non-Autonomous Composite Systems [J]. Acta mathematica scientia,Series A, 2021, 41(5): 1545-1554. |
[11] | Qiaoyi Xiao,Chunqiu Li. Invariant Borel Probability Measures for the Discrete Three Component Reversible Gray-Scott Model [J]. Acta mathematica scientia,Series A, 2021, 41(2): 523-537. |
[12] | Kaixuan Zhu,Yongqin Xie,Feng Zhou,Xijun Deng. Pullback Attractors for the Complex Ginzburg-Landau Equations with Delays [J]. Acta mathematica scientia,Series A, 2020, 40(5): 1341-1353. |
[13] | Lan Xu. Another Proof of Variational Principle for Sub-Additive Potentials [J]. Acta mathematica scientia,Series A, 2020, 40(4): 977-982. |
[14] | Zongfei Han,Shengfan Zhou. Random Exponential Attractor for Non-Autonomous Stochastic FitzHugh-Nagumo System with Multiplicative Noise in R3 [J]. Acta mathematica scientia,Series A, 2020, 40(3): 756-783. |
[15] | Yi Shao,Chunxiang A. Limit Cycles Bifurcations of Liénard System of Degree Four with One Nilpotent Cusp [J]. Acta mathematica scientia,Series A, 2020, 40(3): 619-630. |
Viewed | ||||||||||||||||||||||||||||||||||||||||||||||||||
Full text 260
|
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Abstract 203
|
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Cited |
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Shared | ||||||||||||||||||||||||||||||||||||||||||||||||||
Discussed |
|