Hénon map - Wikipedia
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. The Hénon map takes a point (xn, yn) in …
Hénon Map -- from Wolfram MathWorld
2025年1月14日 · There are at least two maps known as the Hénon map. The first is the two-dimensional dissipative quadratic map given by the coupled equations x_(n+1) = 1-alphax_n^2+y_n (1) y_(n+1) = betax_n (2) (Hénon 1976). The strange attractor illustrated above is obtained for alpha=1.4 and beta=0.3.
Motivated by the Lorenz equations, H ́enon introduced a simple two dimensional map in 1976 [1], which captured the stretch-ing and folding dynamics of chaotic systems such as the Lorenz system.
1. The Henon map - robert-doerner.de
Like the logistic map the Hénon system is a system with a discrete time scale n=1, 2, ... (i. e. it is a map). Whereas the logistic map maps a one-dimensional real interval [0..1] onto itself, the Hénon map is defined on the two-dimensional real plane.
Hénon Map - an overview | ScienceDirect Topics
One may simply define a Hénon map as a diffeomorphism H = H 1 x, y, H 2 x, y with inverse G (x, y) = (G 1 (x, y), G 2 (x, y)) such that all the maps F i x, y, G i x, y are polynomials of degree at most two.
The map T(x;y) = (x2 + c by;x) with parameter b;c is called the Henon map. For For b = 0, the map can be understood by a the one-dimensional quadratic map f(x) = x 2 +c.
Hénon Maps: A List of Open Problems | Arnold Mathematical …
2024年8月13日 · We propose a set of questions on the dynamics of Hénon maps from the real, complex, algebraic and arithmetic points of view.
HENON MAPS: A LIST OF OPEN PROBLEMS´ by Julia X´enelkis de H enon´ Abstract. — We propose a set of questions on the dynamics of Henon maps from the real, com-´ plex, algebraic and arithmetic points of view. Contents 1. Introduction (C. Favre, T. Firsova, L. Palmisano, J. Raissy, and G. Vigny
The Henon map - Vrije Universiteit Amsterdam
Points of a small circle around (x, y) are mapped into an ellipse around (x', y'). E.g. for real eigenvalues of the matrix J. principal axis of this ellipse coinside with eigenvectors of the matrix and deformation of the initial circle is determined by the λ1,2 values.
The Hénon Map - Cornell University
The Hénon map has two parameters (a,c) and is written as follows: Complex Parameter space pictures with SaddleDrop. Compare complex parameter space pictures from various Papadantonakis programs. Real Parameter space pictures; Dynamical space pictures Unstable Manifold Slices; Siegel Balls. Monodromy
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