Bifurcations in the Lozi map

We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.

[1]  Robert L. Devaney,et al.  The Dynamics of a Piecewise Linear Map and its Smooth Approximation , 1997 .

[2]  M. Hénon,et al.  A two-dimensional mapping with a strange attractor , 1976 .

[3]  J. Yorke,et al.  Chaos: An Introduction to Dynamical Systems , 1997 .

[4]  Laura Gardini,et al.  Growing through chaotic intervals , 2008, J. Econ. Theory.

[5]  Robert L. Devaney,et al.  A piecewise linear model for the zones of instability of an area-preserving map , 1984 .

[6]  C. Budd,et al.  Review of ”Piecewise-Smooth Dynamical Systems: Theory and Applications by M. di Bernardo, C. Budd, A. Champneys and P. 2008” , 2020 .

[7]  Sandra Vinagre,et al.  The Basin of Attraction of Lozi Mappings , 2009, Int. J. Bifurc. Chaos.

[8]  James A. Yorke,et al.  Border-collision bifurcations including “period two to period three” for piecewise smooth systems , 1992 .

[9]  Michał Misiurewicz,et al.  STRANGE ATTRACTORS FOR THE LOZI MAPPINGS , 1980 .

[10]  R. Lozi UN ATTRACTEUR ÉTRANGE (?) DU TYPE ATTRACTEUR DE HÉNON , 1978 .

[11]  M. A. Aziz-Alaoui,et al.  Dynamics of a Hénon–Lozi-type map , 2001 .

[12]  Celso Grebogi,et al.  Border collision bifurcations in two-dimensional piecewise smooth maps , 1998, chao-dyn/9808016.

[13]  J. Oteo,et al.  Dynamics of a map with a power-law tail , 2008, 0812.4551.

[14]  Laura Gardini,et al.  Degenerate bifurcations and Border Collisions in Piecewise Smooth 1D and 2D Maps , 2010, Int. J. Bifurc. Chaos.

[15]  Julien Clinton Sprott,et al.  A new simple 2-D piecewise linear map , 2010, J. Syst. Sci. Complex..