The rule is defined by a function $f$, and the evolution is given by: $$ x_n+1 = f(x_n) $$ This is called a map because it maps the state space onto itself.
Discrete systems model change as an iterative process occurring at specific, countable time intervals. The rule is defined by a function $f$,
Dynamical systems provide a mathematical framework for modeling how states change over time. This field is broadly divided into two categories: systems, which evolve smoothly through time, and discrete systems, which change in distinct steps. 1. Continuous Dynamical Systems which evolve smoothly through time
The search keyword asks for "continuous and discrete" because no introduction is complete without understanding the profound connection between them. and discrete systems