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. The action of the map is … Visa mer The horseshoe map f is a diffeomorphism defined from a region S of the plane into itself. The region S is a square capped by two semi-disks. The codomain of $${\displaystyle f}$$ (the "horseshoe") is a proper subset of its … Visa mer • Baker's map • Hénon map Visa mer • "Smale Horseshoe". Scholarpedia. • Evgeny Demidov (2007). "Homoclinic structures in the standard map". ibiblio.org. Retrieved 2016-07-11. • ChaosBook.org Chapter "Stretch, fold, prune" Visa mer The horseshoe map was designed to reproduce the chaotic dynamics of a flow in the neighborhood of a given periodic orbit. The neighborhood is chosen to be a small disk perpendicular to the orbit. As the system evolves, points in this disk remain close to the … Visa mer Webb24 mars 2024 · The Smale horseshoe map consists of a sequence of operations on the unit square. First, stretch in the direction by more than a factor of two, then compress in …
AppDynSys : Smale Horseshoe : Iteration - YouTube
Webb20 okt. 2024 · In 1960 Stephen Smale (building on work by David Birkhoff) proved that the horseshoe is in some sense universal. A large class of dynamical systems, defined by mathematical equations, contain the dynamics of the horseshoe map and therefore also contain its chaos. Everything hinges on the existence of a particular point. WebbThe Smale Horseshoe We will begin our study of “chaotic dynamics” by describing and analyzing a two-dimensional map possessing an invariant set having a delightfully … mechanism of action of hypnotic and sedatives
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WebbThe remarkable property of the Smale horseshoe is its stability to perturbations: the symbolic dynamics may be introduced even in the case of a notably deformed … Webb13 dec. 2024 · The horseshoe map is continuous and injective on R 2. In W, it contracts distances horizontally by δ < 1 / 2 and expands vertically by 1 / δ. Outside W, the only … Webb25 okt. 2024 · Smale introduced the horseshoe region for showing that certain diffeomorphisms have infinitely many periodic points, which implied that the map on the … mechanism of action of fluphenazine