## Chaos Theory

*professor Marcel A. Savi, Universidad Federal Rio de Janeiro (Brasil) “Chaos Theory”: 25/1/2024, at 15:00; “Smart Systems and Structures”: 1/2/2024, at 15:00*

Giovedì 25 Gennaio 2024, ore 15:00

This presentation presents an overview of chaos theory. It starts

with an historical introduction, passing from the scientific

revolution going to the studies that characterize the modern

chaos. The interdisciplinarity is explored showing different areas

of applications. Afterward, the background of dynamical systems

is of concern, presenting the mathematical representation and

the concept of stability. Chaotic dynamics is then explored from

the horseshoe transformation, establishing that it is a

consequence of the contraction-expansion-fold process. The main

aspects of chaotic behavior are then discussed defining chaotic

and fractal attractors. Routes to chaos are investigated showing

some definitions of bifurcation, treating local and global

bifurcations. Lyapunov exponents are defined in order to present

a diagnostic tool for chaos.