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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 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. Maps may be parameterized by a discrete-time or a continuous-time parameter.
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 .
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 ...
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.
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
Orbits of the standard map for K = 1.2. Orbits of the standard map for K = 2.0. The large green region is the main chaotic region of the map. A single orbit of the standard map for K=2.0. Magnified close-up centered at =, p = 0.666, of total width/height 0.02. Note the extremely uniform distribution of the orbit.
Hénon attractor for a = 1.4 and b = 0.3 Hénon attractor for a = 1.4 and b = 0.3. In mathematics, the Hénon map, sometimes called Hénon–Pomeau attractor/map, [1] is a discrete-time dynamical system. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior.