000			nam a22 4500
999			_c32424 _d32424
008			230831b xxu||||| |||| 00| 0 eng d
020			_a9783031251535
082			_a003 _bDIL
100			_aDilao, Rui
245			_aDynamical system and chaos : an introduction with applications
260			_bSpringer, _c2023 _aCham :
300			_aix, 326 p. ; _bill., _c24 cm
365			_d84.99 _bEUR _c94.90
490			_aUNITEXT for physics
504			_aIncludes bibliographical references and index.
520			_aThis 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.
650			_aBifurcation diagram
650			_aCellular automation
650			_aDifference equation
650			_aFixed point
650			_aHenon map
650			_aHyperbolic fixed point
650			_aLimit cycle
650			_aLorenz equations
650			_a Lyapunov exponents
650			_aPhase space
650			_aPoincare map
650			_aThree- body problem
650			_aUnstable manifolds
650			_aFractal sets
942			_2ddc _cBK