American Institute of Mathematical Sciences

Advanced
September  2009, 25(3): 777-795. doi: 10.3934/dcds.2009.25.777

Minimal dynamical systems on a discrete valuation domain

Jean-Luc Chabert 1, , Ai-Hua Fan 1, and  Youssef Fares 1,

1. 

LAMFA, UMR 6140, CNRS, University of Picardie, 33 Rue Saint Leu, 80039 Amiens, France, France, France

Received  July 2008 Revised  February 2009 Published  August 2009

We consider isometric dynamical systems on a Legendre set of a discrete valuation domain with finite residual field. We characterize the minimality of the system by using the structure sequence of the Legendre set and also find the corresponding adding machine to which such a minimal system is conjugate. The minimality of affine maps acting on the domain or on the group of units is fully studied.
Keywords: discrete dynamics, discrete valuation domain..
Mathematics Subject Classification: Primary: 37B05; Secondary: 11K3.
Citation: Jean-Luc Chabert, Ai-Hua Fan, Youssef Fares. Minimal dynamical systems on a discrete valuation domain. Discrete & Continuous Dynamical Systems, 2009, 25 (3) : 777-795. doi: 10.3934/dcds.2009.25.777
[1]

Yuri N. Fedorov, Dmitry V. Zenkov. Dynamics of the discrete Chaplygin sleigh. Conference Publications, 2005, 2005 (Special) : 258-267. doi: 10.3934/proc.2005.2005.258
[2]

David Iglesias-Ponte, Juan Carlos Marrero, David Martín de Diego, Edith Padrón. Discrete dynamics in implicit form. Discrete & Continuous Dynamical Systems, 2013, 33 (3) : 1117-1135. doi: 10.3934/dcds.2013.33.1117
[3]

Wei Wang, Anthony Roberts. Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain. Discrete & Continuous Dynamical Systems, 2011, 31 (1) : 253-273. doi: 10.3934/dcds.2011.31.253
[4]

Yicang Zhou, Paolo Fergola. Dynamics of a discrete age-structured SIS models. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 841-850. doi: 10.3934/dcdsb.2004.4.841
[5]

Anatoli F. Ivanov. On global dynamics in a multi-dimensional discrete map. Conference Publications, 2015, 2015 (special) : 652-659. doi: 10.3934/proc.2015.0652
[6]

Gabriella Bretti, Ciro D’Apice, Rosanna Manzo, Benedetto Piccoli. A continuum-discrete model for supply chains dynamics. Networks & Heterogeneous Media, 2007, 2 (4) : 661-694. doi: 10.3934/nhm.2007.2.661
[7]

André Nachbin. Discrete and continuous random water wave dynamics. Discrete & Continuous Dynamical Systems, 2010, 28 (4) : 1603-1633. doi: 10.3934/dcds.2010.28.1603
[8]

César M. Silva. Admissibility and generalized nonuniform dichotomies for discrete dynamics. Communications on Pure & Applied Analysis, 2021, 20 (10) : 3419-3443. doi: 10.3934/cpaa.2021112
[9]

Masaki Sekiguchi, Emiko Ishiwata, Yukihiko Nakata. Dynamics of an ultra-discrete SIR epidemic model with time delay. Mathematical Biosciences & Engineering, 2018, 15 (3) : 653-666. doi: 10.3934/mbe.2018029
[10]

Ming Chen, Hao Wang. Dynamics of a discrete-time stoichiometric optimal foraging model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 107-120. doi: 10.3934/dcdsb.2020264
[11]

Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183
[12]

Sungwoo Ahn, Winfried Just. Digraphs vs. dynamics in discrete models of neuronal networks. Discrete & Continuous Dynamical Systems - B, 2012, 17 (5) : 1365-1381. doi: 10.3934/dcdsb.2012.17.1365
[13]

Alfonso Artigue. Discrete and continuous topological dynamics: Fields of cross sections and expansive flows. Discrete & Continuous Dynamical Systems, 2016, 36 (11) : 5911-5927. doi: 10.3934/dcds.2016059
[14]

Matteo Focardi, Paolo Maria Mariano. Discrete dynamics of complex bodies with substructural dissipation: Variational integrators and convergence. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 109-130. doi: 10.3934/dcdsb.2009.11.109
[15]

Alexander J. Zaslavski. The turnpike property of discrete-time control problems arising in economic dynamics. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 861-880. doi: 10.3934/dcdsb.2005.5.861
[16]

S. Mohamad, K. Gopalsamy. Neuronal dynamics in time varying enviroments: Continuous and discrete time models. Discrete & Continuous Dynamical Systems, 2000, 6 (4) : 841-860. doi: 10.3934/dcds.2000.6.841
[17]

Guihong Fan, Gail S. K. Wolkowicz. Chaotic dynamics in a simple predator-prey model with discrete delay. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 191-216. doi: 10.3934/dcdsb.2020263
[18]

Horst R. Thieme. Discrete-time dynamics of structured populations via Feller kernels. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021082
[19]

Mohammadreza Molaei. Hyperbolic dynamics of discrete dynamical systems on pseudo-riemannian manifolds. Electronic Research Announcements, 2018, 25: 8-15. doi: 10.3934/era.2018.25.002
[20]

Guangyu Sui, Meng Fan, Irakli Loladze, Yang Kuang. The dynamics of a stoichiometric plant-herbivore model and its discrete analog. Mathematical Biosciences & Engineering, 2007, 4 (1) : 29-46. doi: 10.3934/mbe.2007.4.29

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (81)
  • HTML views (0)
  • Cited by (14)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy