Critical sets and two-dimensional topologically mixing attractors of a pair of coupled ''tent maps'' (Q1974355)

The author deals with a two-parameter family of piecewise linear endomorphisms of the plane of the form \[ F: (x,y)\mapsto (1- a(1- b)|x|- ab|y|,1- a(1- b)|y|- ab|x|),\tag{1} \] where the parameters \(a\) and \(b\) are such that \(0< a< 2\) and \(0< b< 1\). The author proves that for any \(a\in ({1+ \sqrt 5\over 2},2)\) and \(b\in (0,(a-1)/2a)\), the map \(F\) defined by (1) has a chaotic strange attractor \(\Lambda\), on which the map \(F\) is topologically mixing.