Abstract
Maps…
Let ƒ be a diffeomorphism of the plane. A periodic point of ƒ is a point P such that. This periodic point is a saddle if the Jacobian matrix of ƒn at P has one eigenvalue out of the unit circle, and one inside. A saddle has two invariant manifolds: the stable manifold of P is the set of points WI, whose orbits converge to P as m→co, the unstable manifold of P is the set of points Wp whose orbits converge to P as m→co. If ƒ maps the 2-disk D2 into itself, we call the restriction of ƒ to D2 a smooth embedding, and still denote by f the new map.
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© 1991 Springer Science+Business Media Dordrecht
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Gambaudo, JM., Tresser, C. (1991). How Horseshoes are Created. In: Tirapegui, E., Zeller, W. (eds) Instabilities and Nonequilibrium Structures III. Mathematics and Its Applications, vol 64. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3442-2_2
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DOI: https://doi.org/10.1007/978-94-011-3442-2_2
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