
Mathematics 2015
Symmetric band complexes of thin type and chaotic sections which are not quite chaoticAbstract: In a recent paper we constructed a family of foliated 2complexes of thin type whose typical leaves have two topological ends. Here we present simpler examples of such complexes that are, in addition, symmetric with respect to an involution and have the smallest possible rank. This allows for constructing a 3periodic surface in the threespace with a plane direction such that the surface has a central symmetry, and the plane sections of the chosen direction are chaotic and consist of infinitely many connected components. Moreover, typical connected components of the sections have an asymptotic direction, which is due to the fact that the corresponding foliation on the surface in the 3torus is not uniquely ergodic.
