Abstract

We study the topological attractors of injective piecewise contracting maps on a compact interval with any finite number N ≥ 2 of continuity pieces. We prove the existence of a “spectral decomposition” of the attractor into a finite number of transitive components that are either periodic orbits or Cantor sets. In the non-generic case, we prove that some orbits accumulate at both sides of the discontinuities points, and that this phenomenon generates the transitive Cantor sets of the attractor