From ce6895072faed498308254713fb54cdd7d466100 Mon Sep 17 00:00:00 2001 From: Sergiu Ivanov Date: Tue, 9 Apr 2024 14:20:54 +0200 Subject: [PATCH] Say that I will mostly use discrete dynamical systems. --- deal.tex | 13 +++++++++++++ 1 file changed, 13 insertions(+) diff --git a/deal.tex b/deal.tex index 681fe50..e589e25 100644 --- a/deal.tex +++ b/deal.tex @@ -550,6 +550,19 @@ reaching $s$. If $T = \mathbb{N}$, then the trajectory through $s$ is the iteration of $F$: $\{F^k(s) \mid k \in \mathbb{N}\}$, where $F^0(s) = s$, $F^1(s) = F(s)$, $F^2(s) = F(F(s))$, etc. +While I will give most of the general definitions for abstract +dynamical systems, I will rely on discrete-time dynamical systems +later on in the manuscript, for the following reasons: +\begin{enumerate} +\item discrete time yields simpler formal systems, which can capture + a wider range of features before becoming too complex to comprehend, +\item discrete time is sufficient to represent the majority of + time-related concepts, e.g., event ordering, situating measurements + in time, etc. +\end{enumerate} +Last but not least, this choice is motivated by my own expertise as +a computer scientist lying in the field of discrete dynamical systems. + \printbibliography[heading=subbibliography] \end{refsection}