Lyapunov exponent of second degree polynomi̇al functi̇ons

One of the fundamental characteristics of chaos is its sensitive dependence on initial conditions. Lyapunov exponent, which is a measure of sensitive dependence on initial conditions, is one of the most important indicators of chaoticness. In this thesis, whether discrete dynamic systems are chaotic or not is examined in detail with the help of Lyapunov exponent. Firstly, the necessary basic definitions and theorems about Lyapunov exponent, discrete dynamic systems and chaos are given, and Lyapunov exponent values are determined on some examples. Lyapunov exponent values of second-order chaotic functions and Lyapunov exponent values of some piecewise linear functions were examined. In Susan Bassein's article, whether piecewise linear functions are chaotic or not is determined based on the definition of chaos depending on the parameter. In this study, similar results are obtained depending on the parameter by changing the Lyapunov exponents of the same function family. It has been investigate how Lyapunov exponents change when appropriate parabola curves are selected instead of line segments.