scholarly journals Relation Between Discrete-Time Linear Representation Systems and Affine Dynamical Systems

1981 ◽  
Vol 17 (3) ◽  
pp. 350-357 ◽  
Author(s):  
Shigeru NIINOMI ◽  
Tsuyoshi MATSUO
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Linear Representation ◽  
Representation Systems ◽  
Time Linear

Discrete-Time Linear Dynamical Systems

2013 ◽  
pp. 133-164
Author(s):  
Brigitte d’Andréa-Novel ◽  
Michel De Lara
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Linear Dynamical Systems ◽  
Time Linear

Structural stability of linear random dynamical systems

1996 ◽  
Vol 16 (6) ◽  
pp. 1207-1220 ◽  
Author(s):  
Nguyen Dinh Cong
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Structural Stability ◽  
Discrete Time ◽  
Random Dynamical Systems ◽  
Random Dynamical System ◽  
Time Linear ◽  
Structurally Stable

AbstractIn this paper, structural stability of discrete-time linear random dynamical systems is studied. A random dynamical system is called structurally stable with respect to a random norm if it is topologically conjugate to any random dynamical system which is sufficiently close to it in this norm. We prove that a discrete-time linear random dynamical system is structurally stable with respect to its Lyapunov norms if and only if it is hyperbolic.

scholarly journals What’s decidable about linear loops?

2022 ◽  
Vol 6 (POPL) ◽  
pp. 1-25
Author(s):  
Toghrul Karimov ◽  
Engel Lefaucheux ◽  
Joël Ouaknine ◽  
David Purser ◽  
Anton Varonka ◽  
...  
Keyword(s):  
Number Theory ◽  
Dynamical Systems ◽  
Model Checking ◽  
Discrete Time ◽  
Three Dimensional ◽  
Dimensional Subspace ◽  
Intrinsic Dimension ◽  
Linear Dynamical Systems ◽  
Polynomial Inequalities ◽  
Time Linear

We consider the MSO model-checking problem for simple linear loops, or equivalently discrete-time linear dynamical systems, with semialgebraic predicates (i.e., Boolean combinations of polynomial inequalities on the variables). We place no restrictions on the number of program variables, or equivalently the ambient dimension. We establish decidability of the model-checking problem provided that each semialgebraic predicate either has intrinsic dimension at most 1, or is contained within some three-dimensional subspace. We also note that lifting either of these restrictions and retaining decidability would necessarily require major breakthroughs in number theory.

Sign in / Sign up

Export Citation Format

Share Document