scolobb/hdr
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity

Define the state graph.

Browse source
This commit is contained in:
Sergiu Ivanov 2024-04-09 09:00:29 +02:00
parent f459d369ef
commit b515d36b79
1 changed files with 4 additions and 1 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

5
deal.tex
View file

@ -534,7 +534,10 @@ $t$ steps, while $\Phi(s, -t)$ can be seen as the state the system
to see the discrete-time dynamical systems as the function to see the discrete-time dynamical systems as the function
$F : X \to X$, giving the state to which the dynamical system $F : X \to X$, giving the state to which the dynamical system
transitions from state $s \in X$: $F(s) = \Phi(s, 1)$ transitions from state $s \in X$: $F(s) = \Phi(s, 1)$
(e.g,~\cite[Chapter~1]{Riva22}). (e.g,~\cite[Chapter~1]{Riva22}). $F$~generates the possibly infinite
state graph of the discrete-time dynamical system, whose nodes are the
states, and there is a directed edge from state $s_1$ to state $s_2$
if $s_2 = F(s_1)$.
Given a dynamical system $\Phi : X \times T \to X$ and a state Given a dynamical system $\Phi : X \times T \to X$ and a state
$s \in X$, it is possible to construct the restricted function $s \in X$, it is possible to construct the restricted function