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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 .
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]
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More precisely, this example works to explain a kind of math called chaos theory, which looks at how small changes made to a system’s initial conditions—like the extra gust of wind from a ...
Pages in category "Chaos theory" The following 65 pages are in this category, out of 65 total. This list may not reflect recent changes. ...
In physics, relativistic chaos is the application of chaos theory to dynamical systems described primarily by general relativity, and also special relativity. Barrow (1982) showed that the Einstein equations exhibit chaotic behaviour and modelled the Mixmaster universe as a dynamical system.
In physics, the Fermi–Pasta–Ulam–Tsingou (FPUT) problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi–Pasta–Ulam–Tsingou recurrence (or Fermi–Pasta–Ulam recurrence) – instead of the expected ergodic behavior.
[4] As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. [5] In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory.