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Homoclinic tangencies to resonant saddles and discrete Lorenz attractors | | S.V. Gonchenko
; I.I.Ovsyannikov
; | | Date: |
1 Sep 2015 | | Abstract: | We study bifurcations of periodic orbits in three parameter general
unfoldings of certain types quadratic homoclinic tangencies to saddle fixed
points. We apply the rescaling technique to first return (Poincar’e) maps and
show that the rescaled maps can be brought to a map asymptotically close to the
3D Henon map $ar x=y,ar y=z,ar z = M_1 + M_2 y + B x - z^2$ which, as
known, exhibits wild hyperbolic Lorenz-like attractors in some open domains of
the parameters. Based on this, we prove the existence of infinite cascades of
Lorenz-like attractors. | | Source: | arXiv, 1509.0264 | | Services: | Forum | Review | PDF | Favorites | |
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