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Starting from the hierarchy of chaos initially proposed by one of us, we systematized the description of chaotic regimes observed in three- and four-dimensional spaces, which cover a large variety of known (and less known) examples of chaos. Starting with the spectrum of Lyapunov exponents as the first taxonomic ranks, we extended the description to higher ranks with some concepts inherited from topology (bounding torus, surface of section, first-return map, \u2026).<\/jats:p><jats:p>By treating extensively the R\u00f6ssler and the Lorenz attractors, we extended the description of branched manifold \u2014 the highest known taxonomic rank for classifying chaotic attractor \u2014 by a linking matrix (or linker) to multicomponent attractors (bounded by a torus whose genus [Formula: see text]).<\/jats:p>","DOI":"10.1142\/s021812742230004x","type":"journal-article","created":{"date-parts":[[2022,2,23]],"date-time":"2022-02-23T10:36:43Z","timestamp":1645612603000},"source":"Crossref","is-referenced-by-count":17,"title":["Dynamical Taxonomy: Some Taxonomic Ranks to Systematically Classify Every Chaotic Attractor"],"prefix":"10.1142","volume":"32","author":[{"given":"Christophe","family":"Letellier","sequence":"first","affiliation":[{"name":"Rouen Normandie University \u2014 CORIA, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray, France"}]},{"given":"Nataliya","family":"Stankevich","sequence":"additional","affiliation":[{"name":"Laboratory of Topological Methods in Dynamics, National Research University Higher School of Economics, Bolshaya Pecherskaya Str., 25\/12, Nizhny Novgorod 603155, Russia"}]},{"given":"Otto E.","family":"R\u00f6ssler","sequence":"additional","affiliation":[{"name":"Division of Theoretical Chemistry, University of T\u00fcbingen, D-72076 T\u00fcbingen, Germany"}]}],"member":"219","published-online":{"date-parts":[[2022,2,22]]},"reference":[{"key":"S021812742230004XBIB001","doi-asserted-by":"publisher","DOI":"10.1134\/1.2121837"},{"key":"S021812742230004XBIB002","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(83)90272-4"},{"key":"S021812742230004XBIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499000729"},{"key":"S021812742230004XBIB004","doi-asserted-by":"publisher","DOI":"10.1142\/0674"},{"key":"S021812742230004XBIB005","volume-title":"Dynamical Systems","author":"Birkhoff G. 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