RT Journal Article T1 Periods of strongly continuous semigroups A1 Muñoz-Fernández, Gustavo A. A1 Seoane-Sepúlveda, Juan B. A1 Weber, Andress AB In this paper, we study the set of periods of (chaotic) strongly continuous semigroups. We prove a relationship between eigenvalues on the imaginary axis of the generator of a strongly continuous semigroup and the set of periods of the semigroup itself. This relationship in turn is used to obtain information about the structure of the set of periods and to construct (chaotic) semigroups with prescribed periods. PB London Mathematical Society SN 1469-2120 YR 2012 FD 2012 LK https://hdl.handle.net/20.500.14352/42552 UL https://hdl.handle.net/20.500.14352/42552 LA eng NO K. Ali Akbar, V. Kannan, S. Gopal and P. Chiranjeevi, ‘The set of periods of periodic points of a linear operator’,Linear Algebra Appl. 431 (2009) 241–246. R.M. Aron, J. B. Seoane-Sepulveda and A. Weber, ‘Chaos on function spaces’, Bull. Aust. Math. Soc.71 (2005) 411–415.F. Bayart and T. Bermudez, ‘Semigroups of chaotic operators’, Bull. London Math. Soc. 41 (2009)823–830.F. Bayart and S. Grivaux, ‘Hypercyclicity and unimodular point spectrum’, J. Funct. Anal. 226 (2005)281–300.J. A. Conejero and E. M. Mangino, ‘Hypercyclic C0-semigroups generated by Ornstein–Uhlenbeck operators’,Mediterr. J. Math. 7 (2010) 101–109.J. A. Conejero, F. Martinez and A. Peris, ‘Sets of periods for linear operators’, Preprint.W. Desch, W. Schappacher and G. F. Webb, ‘Hypercyclic and chaotic semigroups of linear operators’,Ergodic Theory Dynam. Systems 17 (1997) 793–819.G. Kalish, ‘On operators on separable Banach spaces with arbitrary prescribed point spectrum’, Proc.Amer. Math. Soc. 34 (1972) 207–208.R. deLaubenfels and H. Emamirad, ‘Chaos for functions of discrete and continuous weighted shift operators’, Ergodic Theory Dynam. Systems 21 (2001) 1411–1427. A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences 44 (Springer, New York, 1983).O. G. Smolyanov and S. A. Shkarin, ‘On the structure of the spectra of linear operators in Banach spaces’, Mat. Sb. 192 (2001) 99–114. NO Spanish Ministry of Science and Innovation DS Docta Complutense RD 8 may 2024