Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods

Abstract

We describe topological dynamics over a space by starting
from a simple ODE emerging out of two coupled variables. We describe
the dynamics of the evolution of points in space within the deterministic
and stochastic frameworks. Historically dynamical systems were associated
with celestial mechanics. The core philosophies of two kinds
of dynamics emerging from Poincaré and Lyapunov are described.
Smale’s contributions are highlighted. Markovian models are considered.
Semi-group actions are a tool in this study