## The Chaos Theory

### Question 1

What is the definition of the Chaos Theory

### Question 2

How important is the Chaos Theory in order to describe physical systems

### Question 3

What are the problems with the Chaos Theory

### Purpose

The purpose of those two questions is to challenge the importance of the chaos theory.
How ever before you can discuss you have to agree about the definition of the Chaos theory, what it does and how it relates to actual physical systems.
IMO the importance what it does and its practical value is highly overstated.

• To answer that question you could study: Chaos homepage
In that document we read : Thus, chaos theory lays emphasis not on the disorder of the system--the inherent unpredictability of a system--but on the order inherent in the system--the universal behavior of similar systems. I doubt if that helps.
• You could study: The Nature of Deterministic Chaos
In that document we read:How predictable is a chaotic system? As any deterministic system, it is predictable on a short time scale. But on a long time scale, chaotic systems become unpredictable. Here we read "As any deterministic system". THe question is what do they mean. Are all systems deterministic ? I think that is a very important question.
May be you find the answer behind the TAB: Non linear dynamics There we read: Nonlinear dynamics became famouse because of the possibility of deterministic chaos, i.e., irregular solutions even though the equation of motion is deterministic.
• To see how difficult it is to define Chaos, please study: Chaos by Wolfram Mathworld
Here we read: "chaotic systems are distinguished by sensitive dependence on initial conditions and by having evolution through phase space that appears to be quite random."

• To get an idea please study: Chaos in Dynamical Systems: Second Edition By Edward Ott Here we read at page 2: Under certain conditions the tip of the steel beam was observed to oscillate in a very irregular maner and To show that it is not necessary to invoke such effects, Mon and Holmes considered a simple model for their experiment, namely, the forced Duffing equation in the following form. To read more about this equation please read: Duffing oscillator - Scholarpedia