Upper frequent hypercyclicity and related notions

Akin, E.: Recurrence in topological dynamics. Furstenberg families and Ellis actions. Plenum Press, New York (1997)

Bayart, F., Grivaux, S.: Hypercyclicité: le rôle du spectre ponctuel unimodulaire. C. R. Math. Acad. Sci. Paris 338, 703–708 (2004)

Bayart, F., Grivaux, S.: Frequently hypercyclic operators. Trans. Am. Math. Soc. 358, 5083–5117 (2006)

Bayart, F., Grivaux, S.: Invariant Gaussian measures for operators on Banach spaces and linear dynamics. Proc. Lond. Math. Soc. 3(94), 181–210 (2007)

Bayart, F., Matheron, É.: Dynamics of Linear Operators. Cambridge University Press, Cambridge (2009)

Bayart, F., Ruzsa, I.Z.: Difference sets and frequently hypercyclic weighted shifts. Ergod. Theory Dyn. Syst. 35, 691–709 (2015)

Bès, J., Menet, Q., Peris, A., Puig, Y.: Recurrence properties of hypercyclic operators. Math. Ann. 366, 545–572 (2016)

Brown, T.C., Freedman, A.R.: Arithmetic progressions in lacunary sets. Rocky Mountain J. Math. 17, 587–596 (1987)

Brown, T.C., Freedman, A.R.: The uniform density of sets of integers and Fermat’s last theorem. C. R. Math. Rep. Acad. Sci. Canada 12, 1–6 (1990)

Chen, Z., Li, J., Lü, J.: Point transitivity, $$\Delta $$ Δ -transitivity and multi-minimality. Ergod. Theory Dyn. Syst. 35, 1423–1442 (2015)

Freedman, A.R., Sember, J.J.: Densities and summability. Pac. J. Math. 95, 293–305 (1981)

Fremlin, D.H.: Well-distributed sequences and Banach density. http://www1.essex.ac.uk/maths/people/fremlin/n02j23.pdf (2011)

Furstenberg, H.: Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press, Princeton (1981)

Glasner, E.: Classifying dynamical systems by their recurrence properties. Topol. Methods Nonlinear Anal. 24, 21–40 (2004)

Gottschalk, W.H., Hedlund, G.A.: Topological Dynamics. American Mathematical Society, Providence (1955)

Grekos, G.: On various definitions of density (survey). Tatra Mt. Math. Publ. 31, 17–27 (2005)

Grekos, G., Toma, V., Tomanová, J.: A note on uniform or Banach density. Ann. Math. Blaise Pascal 17, 153–163 (2010)

Grivaux, S., Matheron, É.: Invariant measures for frequently hypercyclic operators. Adv. Math. 265, 371–427 (2014)

Grosse-Erdmann, K.-G., Peris Manguillot, A.: Linear Chaos. Springer, London (2011)

Hindman, N.: On creating sets with large lower density. Discrete Math. 80, 153–157 (1990)

Huang, W., Li, H., Ye, X.: Family independence for topological and measurable dynamics. Trans. Am. Math. Soc. 364, 5209–5242 (2012)

Kalton, N.J., Peck, N.T., Roberts, J.W.: An F-Space Sampler. Cambridge University Press, Cambridge (1984)

Kamthan, P.K., Gupta, M.: Sequence Spaces and Series. Marcel Dekker, New York (1981)

Koosis, P.: The Logarithmic Integral I. Cambridge University Press, Cambridge (1998)

Kyrezi, I., Nestoridis, V., Papachristodoulos, C.: Some remarks on abstract universal series. J. Math. Anal. Appl. 387, 878–884 (2012)

Li, J.: Transitive points via Furstenberg family. Topol. Appl. 158, 2221–2231 (2011)

Martínez-Giménez, F., Peris, A.: Chaos for backward shift operators. Int. J. Bifur. Chaos Appl. Sci. Eng. 12, 1703–1715 (2002)

Menet, Q.: Linear chaos and frequent hypercyclicity. Trans. Am. Math. Soc. 369, 4977–4994 (2017)

Moothathu, T.K.S.: Two remarks on frequent hypercyclicity. J. Math. Anal. Appl. 408, 843–845 (2013)

Mouze, A., Munnier, V.: On the frequent universality of the classical universal Taylor series in the complex plane. Glasg. Math. J. 59, 109–117 (2017)

Murillo-Arcila, M., Peris, A.: Strong mixing measures for linear operators and frequent hypercyclicity. J. Math. Anal. Appl. 398, 462–465 (2013)

Papachristodoulos, C.: Upper and lower frequently universal series. Glasg. Math. J. 55, 615–627 (2013)

Peris, A.: Topologically ergodic operators. In: Function Theory on Infinite Dimensional Spaces IX, (Conference, Madrid). http://www.mat.ucm.es/~confexx/web_confe_05/index.htm (2005)

Pólya, G.: Untersuchungen über Lücken und Singularitäten von Potenzreihen. Math. Z. 29, 549–640 (1929)

Rudin, W.: Functional Analysis. McGraw-Hill, New York (1973)

Šalát, T., Toma, V.: A classical Olivier’s theorem and statistical convergence. Ann. Math. Blaise Pascal 10, 305–313 (2003)

Shkarin, S.: On the spectrum of frequently hypercyclic operators. Proc. Am. Math. Soc. 137, 123–134 (2009)

Xiong, J.-C., Lü, J., Tan, F.: Furstenberg family and chaos. Sci. China Ser. A 50, 1325–1333 (2007)