Geodesic
On the existence of infinitely many stable and unstable invariant tori for systems from Newhouse regions with heteroclinic tangencies
Russian journal of nonlinear dynamics, Tome 2 (2006) no. 1, pp. 3-25 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let a $C^r$-smooth ($r\geq 5$) two-dimensional diffeomorphism $f$ have a non-transversal heteroclinic cycle containing several saddle periodic and heteroclinic orbits and, besides, some of the heteroclinic orbits are non-transversal, i.e. at the points of these orbits the invariant manifolds of the corresponding saddles intersect non-transversally. Suppose that a cycle contains at least two saddle periodic orbits such that the saddle value (the absolute value of product of multipliers) of one orbit is less than 1 and it is greater than 1 for the other orbit. We prove that in any neighbourhood (in $C^r$-topology) of $f$ in the space of $C^r$-diffeomorphisms, there are open regions (so-called Newhouse regions with heteroclinic tangencies) where diffeomorphisms with infinitely many stable and unstable invariant circles are dense. For three-dimensional flows, this result implies the existence of Newhouse regions where flows having infinitely many stable and unstable invariant two-dimensional tori are dense.
Keywords: nontransversal heteroclinic cycle, Newhouse region, invariant circle. 
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     author = {S. V. Gonchenko and O. V. Sten'kin and L. P. Shilnikov},
     title = {On the existence of infinitely many stable and unstable invariant tori for systems from {Newhouse} regions with heteroclinic tangencies},
     journal = {Russian journal of nonlinear dynamics},
     pages = {3--25},
     year = {2006},
     volume = {2},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2006_2_1_a0/}
}
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S. V. Gonchenko; O. V. Sten'kin; L. P. Shilnikov. On the existence of infinitely many stable and unstable invariant tori for systems from Newhouse regions with heteroclinic tangencies. Russian journal of nonlinear dynamics, Tome 2 (2006) no. 1, pp. 3-25. http://geodesic.mathdoc.fr/item/ND_2006_2_1_a0/