Dynamical system and chaos : an introduction with applications
- Cham : Springer, 2023
- ix, 326 p. ; ill., 24 cm
- UNITEXT for physics .
Includes bibliographical references and index.
This textbook introduces the language and the techniques of the theory of dynamical systems of finite dimension for an audience of physicists, engineers, and mathematicians at the beginning of graduation. Author addresses geometric, measure, and computational aspects of the theory of dynamical systems. Some freedom is used in the more formal aspects, using only proofs when there is an algorithmic advantage or because a result is simple and powerful. The first part is an introductory course on dynamical systems theory. It can be taught at the master's level during one semester, not requiring specialized mathematical training. In the second part, the author describes some applications of the theory of dynamical systems. Topics often appear in modern dynamical systems and complexity theories, such as singular perturbation theory, delayed equations, cellular automata, fractal sets, maps of the complex plane, and stochastic iterations of function systems are briefly explored for advanced students. The author also explores applications in mechanics, electromagnetism, celestial mechanics, nonlinear control theory, and macroeconomy. A set of problems consolidating the knowledge of the different subjects, including more elaborated exercises, are provided for all chapters.
9783031251535
Bifurcation diagram Cellular automation Difference equation Fixed point Henon map Hyperbolic fixed point Limit cycle Lorenz equations Lyapunov exponents Phase space Poincare map Three- body problem Unstable manifolds Fractal sets