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In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior.Maps may be parameterized by a discrete-time or a continuous-time parameter.
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]
For example, the first few terms of this series are 1, 5, 16, 45, 121, 320, 841, 2205 .... [4] (The same equation holds for any unimodular hyperbolic toral automorphism if the eigenvalues are replaced.) Γ is ergodic and mixing, Γ is an Anosov diffeomorphism and in particular it is structurally stable.
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 .
Pages in category "Chaos theory" The following 65 pages are in this category, out of 65 total. This list may not reflect recent changes. ...
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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]