{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T11:52:00Z","timestamp":1649159520038},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,4]]},"abstract":"<jats:p> For invertible, area-contracting planar maps, much work has been done on the study of the crucial role played by certain unstable periodic orbits, distinguished by being \"accessible\", in understanding some global bifurcations such as metamorphoses of basin boundaries and crisis of attractors. In this paper we concentrate on a one-parameter family of H\u00e9non maps whose attractors present a type of discontinuous change characterized by a sudden replacement of the accessible orbits as the parameter is varied. The change is quantified by a jump in the corresponding accessible rotation number. The rotation rate describes a devil's staircase as a function of the parameter. We estimate the Hausdorff dimensions of the H\u00e9non attractors \u2014 via the Mend\u00e8s France fractal dimension \u2014 for the same interval of parameter values. Our purpose is to show the strong connection between these two functions: the variation of the dimension stays minimal for the parameters under the same plateau in the staircase, while it is markedly greater when the parameter moves from one plateau to another. <\/jats:p>","DOI":"10.1142\/s0218127405012697","type":"journal-article","created":{"date-parts":[[2005,7,5]],"date-time":"2005-07-05T14:52:13Z","timestamp":1120575133000},"page":"1329-1346","source":"Crossref","is-referenced-by-count":0,"title":["FRACTAL PARAMETERS FOR THE STUDY OF H\u00c9NON-LIKE ATTRACTORS"],"prefix":"10.1142","volume":"15","author":[{"given":"R.","family":"HANSEN","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Buenos Aires, Av. Paseo Col\u00f3n 850, (1063) Buenos Aires, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. PIACQUADIO","family":"LOSADA","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Buenos Aires, Av. Paseo Col\u00f3n 850, (1063) Buenos Aires, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01223208"},{"key":"rf2","unstructured":"K.\u00a0Alligood and T.\u00a0Sauer, Continuum Theory and Dynamical Systems, Lecture Notes in Pure and Applied Mathematics\u00a0149 (1993)\u00a0pp. 1\u201314."},{"key":"rf3","doi-asserted-by":"crossref","unstructured":"K. T.\u00a0Alligood, T. D.\u00a0Sauer and J. A.\u00a0Yorke, Chaos. An Introduction to Dynamical Systems (Springer-Verlag, NY, 1997)\u00a0pp. 68\u201370, 80.","DOI":"10.1007\/978-3-642-59281-2"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(87)90078-9"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01608556"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7931-5_8"},{"key":"rf9","unstructured":"E.\u00a0Ott, Chaos in Dynamical Systems (Cambridge University Press, 1993)\u00a0p. 277, 295."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402005285"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.83.3629"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.60.378"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405012697","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:03:00Z","timestamp":1565190180000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405012697"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,4]]},"references-count":10,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,4]]}},"alternative-id":["10.1142\/S0218127405012697"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405012697","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,4]]}}}