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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 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
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.
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The term is closely associated with the work of the mathematician and meteorologist Edward Norton Lorenz.
A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8 / 3 . The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz.
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.
Chaos: Making a New Science is a debut non-fiction book by James Gleick that initially introduced the principles and early development of the chaos theory to the public. [1] It was a finalist for the National Book Award [ 2 ] and the Pulitzer Prize [ 3 ] in 1987, and was shortlisted for the Science Book Prize in 1989. [ 4 ]