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Bifurcation Chaos"],"published-print":{"date-parts":[[2021,8]]},"abstract":"<jats:p> Let [Formula: see text] be a nontrivial compact metric space with metric [Formula: see text] and [Formula: see text] be a continuous self-map, [Formula: see text] be the sigma-algebra of Borel subsets of [Formula: see text], and [Formula: see text] be a Borel probability measure on [Formula: see text] with [Formula: see text] for any open subset [Formula: see text] of [Formula: see text]. This paper proves the following results : (1) If the pair [Formula: see text] has the property that for any [Formula: see text], there is [Formula: see text] such that [Formula: see text] for any open subset [Formula: see text] of [Formula: see text] and all [Formula: see text] sufficiently large (where [Formula: see text] is the characteristic function of the set [Formula: see text]), then the following hold : (a) The map [Formula: see text] is topologically ergodic. (b) The upper density [Formula: see text] of [Formula: see text] is positive for any open subset [Formula: see text] of [Formula: see text], where [Formula: see text]. (c) There is a [Formula: see text]-invariant Borel probability measure [Formula: see text] having full support (i.e. [Formula: see text]). (d) Sensitivity of the map [Formula: see text] implies positive lower density sensitivity, hence ergodical sensitivity. (2) If [Formula: see text] for any two nonempty open subsets [Formula: see text], then there exists [Formula: see text] satisfying [Formula: see text] for any nonempty open subset [Formula: see text], where [Formula: see text] there exist [Formula: see text] with [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218127421501510","type":"journal-article","created":{"date-parts":[[2021,8,13]],"date-time":"2021-08-13T13:11:45Z","timestamp":1628860305000},"page":"2150151","source":"Crossref","is-referenced-by-count":1,"title":["Study on Strong Sensitivity of Systems Satisfying the Large Deviations Theorem"],"prefix":"10.1142","volume":"31","author":[{"given":"Risong","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong 524025, P. R. 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