scholarly journals Ruelle zeta functions for finite dynamical systems and Koyama-Nakajima’s $L$-functions

2016 ◽  
Vol 92 (9) ◽  
pp. 107-111
Author(s):  
Yukihiro Hattori ◽  
Hideaki Morita
Keyword(s):  
Dynamical Systems ◽  
Zeta Functions ◽  
Finite Dynamical Systems

scholarly journals Effects of nondenumerable fixed points in finite dynamical systems

2008 ◽  
Vol 18 (1) ◽  
pp. 013124
Author(s):  
Sagar Chakraborty ◽  
J. K. Bhattacharjee
Keyword(s):  
Dynamical Systems ◽  
Fixed Points ◽  
Finite Dynamical Systems

Linear Finite Dynamical Systems

2005 ◽  
Vol 33 (9) ◽  
pp. 2977-2989 ◽  
Author(s):  
René A. Hernández Toledo
Keyword(s):  
Dynamical Systems ◽  
Finite Dynamical Systems

scholarly journals Equivalence Relations on Finite Dynamical Systems

2001 ◽  
Vol 26 (3) ◽  
pp. 237-251 ◽  
Author(s):  
Reinhard Laubenbacher ◽  
Bodo Pareigis
Keyword(s):  
Dynamical Systems ◽  
Equivalence Relations ◽  
Finite Dynamical Systems

scholarly journals Generalized Fredholm determinants and Selberg zeta functions for Axiom A dynamical systems

1996 ◽  
Vol 16 (4) ◽  
pp. 805-819 ◽  
Author(s):  
Hans Henrik Rugh
Keyword(s):  
Dynamical Systems ◽  
Zeta Function ◽  
Complex Plane ◽  
Entire Functions ◽  
Fredholm Determinant ◽  
Three Dimensional ◽  
Zeta Functions ◽  
Selberg Zeta Function ◽  
Fredholm Determinants ◽  
Axiom A

AbstractWe consider a generalized Fredholm determinant d(z) and a generalized Selberg zeta function ζ(ω)−1 for Axiom A diffeomorphisms of a surface and Axiom A flows on three-dimensional manifolds, respectively. We show that d(z) and ζ(ω)−1 extend to entire functions in the complex plane. That the functions are entire and not only meromorphic is proved by a new method, identifying removable singularities by a change of Markov partitions.

scholarly journals On the Rank and Periodic Rank of Finite Dynamical Systems

10.37236/7017 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Maximilien Gadouleau
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Periodic Points ◽  
Boolean Networks ◽  
Finite Alphabet ◽  
Interaction Graph ◽  
Maximum Rank ◽  
Local Functions ◽  
Finite Dynamical Systems ◽  
Finite Dynamical System

A finite dynamical system is a function $f : A^n \to A^n$ where $A$ is a finite alphabet, used to model a network of interacting entities. The main feature of a finite dynamical system is its interaction graph, which indicates which local functions depend on which variables; the interaction graph is a qualitative representation of the interactions amongst entities on the network. The rank of a finite dynamical system is the cardinality of its image; the periodic rank is the number of its periodic points. In this paper, we determine the maximum rank and the maximum periodic rank of a finite dynamical system with a given interaction graph over any non-Boolean alphabet. The rank and the maximum rank are both computable in polynomial time. We also obtain a similar result for Boolean finite dynamical systems (also known as Boolean networks) whose interaction graphs are contained in a given digraph. We then prove that the average rank is relatively close (as the size of the alphabet is large) to the maximum. The results mentioned above only deal with the parallel update schedule. We finally determine the maximum rank over all block-sequential update schedules and the supremum periodic rank over all complete update schedules.

scholarly journals Modeling and Analysis of Germ Layer Formations Using Finite Dynamical Systems

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Alexander Garza ◽  
◽  
Megan Eberle ◽  
Eric A. Eager ◽  
◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Germ Layer ◽  
Modeling And Analysis ◽  
Finite Dynamical Systems
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