Templates and subtemplates of R\"ossler attractors from a bifurcation diagram

We study the bifurcation diagram of the R\"ossler system. It displays the various dynamical regimes of the system (stable or chaotic) when a parameter is varied. We choose a diagram that exhibits coexisting attractors and banded chaos. We use the topological characterization method to study these attractors. Then, we details how the templates of these attractors are subtemplates of a unique template. Our main result is that only one template describe the topological structure of height attractors. This leads to a topological partition of the bifurcation diagram that gives the symbolic dynamic of all bifurcation diagram attractors with a unique template

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