2013/10/15 by Sandra Hayes, Christian Wolf, Hayes, Sandra +1
Mathematics · Physics and Astronomy · #37D15 #37E30 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37D15 #msc:37E30
paper · pdf · doi:10.48550/arxiv.1310.4032
arxiv created 2013/10/15 · openalex publication_date 2013/10/15 · arxiv updated 2013/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the dynamics of a family of diffeomorphisms in \bR2 defined by F(x,y)=(g(x)+h(y),h(x)), where g(x) is a unimodal C2-map which has the same dynamical properties as the logistic map P(x)=μx(1-x), and h(x) is a C2 map which is a small perturbation of a linear map. For certain maps of this form we show that there are exactly two periodic points, namely an attracting fixed point and a saddle fixed point and the boundary of the basin of attraction is the stable manifold of the saddle. The basin boundary also has the same regularity as F, in contrast to the frequently observed fractal nature of basin boundaries. To establish these results we describe the orbits under forward and backward iteration of every point in the plane.