From the Rössler attractor to the templex
Résumé
Methods to accomplish a topological description of the structure of a flow in high-dimensional state space (in more than three dimensions) have a long history, full of partially fruitful attempts, but the ideal mathematical object to achieve this task seems to be what we now call templex. Cell complexes can be traced back to Poincaré’s papers during 1900 and the study of chaotic attractors using cell complexes to the 1990s. Since then, algebraic topology has been regarded as the most promising mathematical formalism to describe chaos beyond three dimensions, overcoming the restrictions that templates, based on the knot content of attractors, cannot represent. In this talk, we present the road leading to the templex starting from the Rössler attractor and ending with a four-dimensional system designed on the basis of a set of equations proposed by Deng.
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