{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:56:55Z","timestamp":1754157415896,"version":"3.41.2"},"reference-count":15,"publisher":"Emerald","issue":"7\/8","license":[{"start":{"date-parts":[[2009,8,7]],"date-time":"2009-08-07T00:00:00Z","timestamp":1249603200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,8,7]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to demonstrate new properties of continuous\u2010 and discrete\u2010time dynamical systems.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>First, definitions of two types of spatial symmetry are introduced. These are used as definitions, which, along with existing knowledge show that it is possible to identify properties of dynamical systems that were previously unknown.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>The main result of the paper is a new theorem regarding new properties of continuous\u2010 and discrete\u2010time dynamical systems.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Research limitations\/implications<\/jats:title><jats:p>The present study provides a starting point for further research on the differences between continuous\u2010 and discrete\u2010time dynamical systems. This work builds on the definition of spatial symmetry.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>The theorem proved in this paper and the new properties of dynamical systems can be used to introduce new methods of approximating continuous\u2010time dynamical systems by discrete\u2010time dynamical systems and vice versa. Such approaches can also be helpful in constructing chaotic sources to model noise.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>This paper offers contributions to the broader discussion of differences between continuous\u2010 and discrete\u2010time dynamical systems. In particular, the paper supports the statement that many discrete\u2010time processes cannot be embedded into continuous ones.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910976880","type":"journal-article","created":{"date-parts":[[2009,10,5]],"date-time":"2009-10-05T10:50:22Z","timestamp":1254739822000},"page":"1171-1181","source":"Crossref","is-referenced-by-count":0,"title":["On some properties of even\u2010symmetric and odd\u2010symmetric dynamical systems"],"prefix":"10.1108","volume":"38","author":[{"given":"Mieczyslaw","family":"Jessa","sequence":"first","affiliation":[]}],"member":"140","reference":[{"key":"key2022021919575425800_b1","doi-asserted-by":"crossref","unstructured":"Chernikov, A.A., Sagdeev, R.Z. and Zaslavski, G.M. (1988), \u201cChaos: how regular can it be?\u201d, Physics Today, Vol. 41 No. 11, pp. 27\u201035.","DOI":"10.1063\/1.881159"},{"key":"key2022021919575425800_b2","doi-asserted-by":"crossref","unstructured":"Chua, L.O. and Lin, G.N. 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