{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:58:07Z","timestamp":1760241487485,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,3,23]],"date-time":"2018-03-23T00:00:00Z","timestamp":1521763200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, using the Poincar\u00e9 section of the flow we numerically verify a generalization of a Pesin-like identity at the chaos threshold of the R\u00f6ssler system, which is one of the most popular three-dimensional continuous systems. As Poincar\u00e9 section points of the flow show similar behavior to that of the logistic map, for the R\u00f6ssler system we also investigate the relationships with respect to important properties of nonlinear dynamics, such as correlation length, fractal dimension, and the Lyapunov exponent in the vicinity of the chaos threshold.<\/jats:p>","DOI":"10.3390\/e20040216","type":"journal-article","created":{"date-parts":[[2018,3,23]],"date-time":"2018-03-23T08:34:53Z","timestamp":1521794093000},"page":"216","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the R\u00f6ssler System"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8384-7498","authenticated-orcid":false,"given":"Kivanc","family":"Cetin","sequence":"first","affiliation":[{"name":"Department of Physics, Faculty of Science, Ege University, 35100 Izmir, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4073-858X","authenticated-orcid":false,"given":"Ozgur","family":"Afsar","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Science, Ege University, 35100 Izmir, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1104-0847","authenticated-orcid":false,"given":"Ugur","family":"Tirnakli","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Science, Ege University, 35100 Izmir, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","article-title":"Deterministic Nonperiodic Flow","volume":"20","author":"Lorenz","year":"1963","journal-title":"J. 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