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The Hénon attractor is a fractal, smooth in one direction and a Cantor set in another. Numerical estimates yield a correlation dimension of 1.21 ± 0.01 or 1.25 ± 0.02 [2] (depending on the dimension of the embedding space) and a Box Counting dimension of 1.261 ± 0.003 [3] for the attractor of the classical map.
Michel Hénon (French:; 23 July 1931, Paris – 7 April 2013, Nice) was a French mathematician and astronomer. [1] He worked for a long time at the Nice Observatory.. In astronomy, Hénon is well known for his contributions to stellar dynamics.
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.
Hénon–Heiles system shows rich dynamical behavior. Usually the Wada property cannot be seen in the Hamiltonian system, but Hénon–Heiles exit basin shows an interesting Wada property.
Visual representation of a strange attractor. [1] Another visualization of the same 3D attractor is this video.Code capable of rendering this is available.. In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, [2] for a wide variety of starting conditions of the system.
Plot of the Duffing map showing chaotic behavior, where a = 2.75 and b = 0.15. Phase portrait of a two-well Duffing oscillator (a differential equation, rather than a map) showing chaotic behavior.
Floris Takens (12 November 1940 – 20 June 2010) [1] was a Dutch mathematician known for contributions to the theory of chaotic dynamical systems.. Together with David Ruelle, he predicted that fluid turbulence could develop through a strange attractor, a term they coined, as opposed to the then-prevailing theory of accretion of modes.
Hausdorff dimension (exact value) Hausdorff dimension (approx.) Name Illustration Remarks Calculated: 0.538: Feigenbaum attractor: The Feigenbaum attractor (see between arrows) is the set of points generated by successive iterations of the logistic map for the critical parameter value =, where the period doubling is infinite.