Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points
Abstract
It was established in [1] 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 nonsimple.
- Publication:
-
Regular and Chaotic Dynamics
- Pub Date:
- July 2014
- DOI:
- 10.1134/S1560354714040054
- arXiv:
- arXiv:1412.0738
- Bibcode:
- 2014RCD....19..495G
- Keywords:
-
- Homoclinic tangency;
- rescaling;
- 3D Hénon map;
- bifurcation;
- Lorenz-like attractor;
- 37C05;
- 37G25;
- 37G35;
- Mathematics - Dynamical Systems;
- 37C05;
- 37G25;
- 37G35
- E-Print:
- Regular and Chaotic Dynamics, 2014, Vol. 19, No. 4, pp. 495-505