Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points

Abstract

It was established in 2006 that bifurcations of three-dimensional diffeomorphisms with a homoclinic tangency to a saddle-focus fixed point with the Jacobian equal to 1 can lead to Lorenz-like strange attractors. In the present paper we prove an analogous result for three-dimensional diffeomorphisms with a homoclinic tangency to a saddle fixed point with the Jacobian equal to 1, provided the quadratic homoclinic tangency under consideration is non-simple.

References in corpus (1)

• Simple scenarios of onset of chaos in three-dimensional maps

Cited by in corpus (2)

• Variety of strange pseudohyperbolic attractors in three-dimensional generalized H'enon maps
• Computer assisted proof of the existence of the Lorenz attractor in the Shimizu-Morioka system