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Bifurcation Chaos"],"published-print":{"date-parts":[[2024,8]]},"abstract":"<jats:p> This paper investigates the Li\u2013Yorke chaos in linear systems with weak topology on Hilbert spaces. A weak topology induced by bounded linear functionals is first constructed. Under this weak topology, it is shown that the weak Li\u2013Yorke chaos can be equivalently measured by an irregular or a semi-irregular vector, which are utilized to establish criteria for the weak Li\u2013Yorke chaos of diagonalizable operators, Jordan blocks, and upper triangular operators. In particular, for a linear operator that can be decomposed into a direct sum of finite-dimensional Jordan blocks, it is Li\u2013Yorke chaotic in weak topology if its point spectrum contains a pair of real opposite eigenvalues with absolute values not less than 1, or a pair of complex conjugate eigenvalues with moduli not less than\u00a01. Interestingly, as a specific example of upper triangular operator, the existence of Li\u2013Yorke chaos in weak topology can be derived for a class of linear operators expressed as the direct sum of finite-dimensional Jordan blocks and a strongly irreducible operator. <\/jats:p>","DOI":"10.1142\/s0218127424501220","type":"journal-article","created":{"date-parts":[[2024,7,20]],"date-time":"2024-07-20T04:36:33Z","timestamp":1721450193000},"source":"Crossref","is-referenced-by-count":2,"title":["Li\u2013Yorke Chaos in Linear Systems with Weak Topology on Hilbert Spaces"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3623-4947","authenticated-orcid":false,"given":"Qigui","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. 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