Basins of periodic orbits for elliptic maps of the torus |
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Authors: | Luciano Amadasi Mario Casartelli |
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Institution: | (1) Dipartimento di Fisica dell'Università di Parma, Parma, Italy;(2) Unità di Parma, CNR-Consorzio INFM, Italy |
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Abstract: | The behavior of basins of periodic orbits, for families of elliptic maps in the 2D torus depending on a parameter, is studied. We give an explicit formula for periodic orbits (i.e., central points of basins), considering also the occurrence of singular situations. Such a formula describes the evolution of basins, showing that onset and disappearance of periodic orbits cannot be reduced to a simple bifurcation scheme. Also, the stochastic features of the strange attractor at the border of ellipticity may be related to the dynamics of collapsing basins. |
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Keywords: | Elliptic maps basins periodic orbits |
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