{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:46:09Z","timestamp":1760888769352},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p> We apply to bidimensional chaotic maps the numerical method proposed by Ginelli et al. [2007] to approximate the associated Oseledets splitting, i.e. the set of linear subspaces spanned by the so-called covariant Lyapunov vectors (CLV) and corresponding to the Lyapunov spectrum. These subspaces are the analog of linearized invariant manifolds for nonperiodic points, so the angles between them can be used to quantify the degree of hyperbolicity of generic orbits; however, such splitting being noninvariant under smooth transformations of phase space, it is interesting to investigate the properties of transversality when coordinates change, e.g. to study it in distinct dynamical systems. To illustrate this issue on the Chirikov\u2013Taylor standard map, we compare the probability densities of transversality for two different coordinate systems; these are connected by a linear transformation that deforms splitting angles through phase space, changing also the probability density of almost-zero angles although complete tangencies are in fact invariant. This is completely due to the PDF transformation law and strongly suggests that any statistical inference from such distributions must be generally taken with care. <\/jats:p>","DOI":"10.1142\/s0218127412502173","type":"journal-article","created":{"date-parts":[[2012,10,16]],"date-time":"2012-10-16T02:49:37Z","timestamp":1350355777000},"page":"1250217","source":"Crossref","is-referenced-by-count":7,"title":["ESTIMATING HYPERBOLICITY OF CHAOTIC BIDIMENSIONAL MAPS"],"prefix":"10.1142","volume":"22","author":[{"given":"MATTEO","family":"SALA","sequence":"first","affiliation":[{"name":"Center for Nonlinear and Complex Systems, Universit\u00e0 dell'Insubria, Via Valleggio 11, Como 22100, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CESAR","family":"MANCHEIN","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Federal do Paran\u00e0, 81531-980 Curitiba, PR, Brazil"},{"name":"Departamento de F\u00edsica, Universidade do Estado de Santa Catarina, 89219-710 Joinville, SC, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ROBERTO","family":"ARTUSO","sequence":"additional","affiliation":[{"name":"Center for Nonlinear and Complex Systems, Universit\u00e0 dell'Insubria, Via Valleggio 11, Como 22100, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,10,15]]},"reference":[{"key":"rf1","first-page":"036210-1","volume":"80","author":"Artuso R.","journal-title":"Phys. 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