On Global Bifurcations of Three-dimensional Diffeomorphisms Leading to Lorenz-like Attractors

S.V. Gonchenko, I.I. Ovsyannikov, L. Lerman, D. Turaev, V. Vougalter, M. Zaks
2013 Mathematical Modelling of Natural Phenomena  
We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransversal heteroclinic cycles. We show that bifurcations under consideration lead to the birth of Lorenz-like attractors. They can be viewed as attractors in the Poincare map for periodically perturbed classical Lorenz attractors and hence they can allow for the existence of homoclinic tangencies and wild hyperbolic sets.
doi:10.1051/mmnp/20138505 fatcat:oor7wehbfjf2hkhdzsqt6c3upa