Toward a general procedure for extracting templates from chaotic attractors bounded by high genus torus

International audienceTopological analysis of chaotic attractor by the mean of template is rather well established for simple attractors like those solution to the Rössler system. Lorenz-like attractors are already slightly more complicated because they are bounded by a genus-3 bounding torus, implying the necessity to use a two-component Poincaré section. In this paper, we enriched the concept of linking matrix to correctly describe algebraically template for attractor with (g-1) components Poincaré section and whose bounding torus has g interior holes aligned. An example with g=5 - a multispiral attractor - is explicitly treated