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Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. [2]
In this book, Stewart explains chaos theory to an audience presumably unfamiliar with it. As the book progresses the writing changes from simple explanations of chaos theory to in-depth, rigorous mathematical study. Stewart covers mathematical concepts such as differential equations, resonance, nonlinear dynamics, and probability. The book is ...
Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory; Brill–Noether theory; Catastrophe theory; Category theory; Chaos theory; Character theory; Choquet theory; Class field theory; Cobordism theory; Coding theory; Cohomology theory ...
In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems . The map was introduced by Stephen Smale while studying the behavior of the orbits of the van der Pol oscillator .
As a pedagogic tool, the Malkus waterwheel became a paradigmatic realization of a chaotic system, and is widely used in the teaching of chaos theory. [3] In addition to its pedagogic use, the Malkus waterwheel has been actively studied by researchers in dynamical systems and chaos. [4] [5] [6] [7]
Devaney is known for formulating a simple and widely used definition of chaotic systems, one that does not need advanced concepts such as measure theory. [8] In his 1989 book An Introduction to Chaotic Dynamical Systems, Devaney defined a system to be chaotic if it has sensitive dependence on initial conditions, it is topologically transitive (for any two open sets, some points from one set ...
Lorenz was born in 1917 in West Hartford, Connecticut. [5] He acquired an early love of science from both sides of his family. His father, Edward Henry Lorenz (1882-1956), majored in mechanical engineering at the Massachusetts Institute of Technology, and his maternal grandfather, Lewis M. Norton, developed the first course in chemical engineering at MIT in 1888.
Ivar Ekeland has written popular books about chaos theory and about fractals, [1] [2] such as the Julia set (animated). Ekeland's exposition provided mathematical inspiration to Michael Crichton's discussion of chaos in Jurassic Park. [3] Ivar I. Ekeland (born 2 July 1944, Paris) is a French mathematician of Norwegian descent.