"http://www.sciencedirect.com/science/article/pii/S0960077913001240" . "10.1016/j.chaos.2013.06.010" . "81239" . . "RIV/47813059:19610/13:#0000396!RIV14-MSM-19610___" . . . "September 2013" . "For a continuous map f : X -> X of a compact metric space, the set IR(f) of irregularly recurrent points is the set of points which are upper density recurrent, but not lower density recurrent. These notions are related to the structure of the measure center, but many problems still remain open. We solve some of them. The main result, based on examples by Obadalova and Smital [Obadalova L, Smltal J. Counterexamples to the open problem by Zhou and Feng on minimal center of attraction. Nonlinearity 2012;25:1443-9], shows that positive topological entropy supported by the center C-z of attraction of a point z is not related to the property that C-z is the support of an invariant measure generated by z. We also show that IR(f) is invariant with respect to standard operations, like f(IR(f)) = IR(f), or IR(f(m)) = IR(f) for m is an element of N."@en . . . "0960-0779" . . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . . . . . . . "Irregular recurrence in compact metric spaces" . "I" . "54" . . "19610" . "RIV/47813059:19610/13:#0000396" . . "Obadalov\u00E1, Lenka" . "1"^^ . "[872EFA7DE967]" . "1"^^ . "recurrence; topological entropy; invariant measures; Banach density"@en . "000324442600013" . . "Chaos, Solitons & Fractals" . "5"^^ . "Irregular recurrence in compact metric spaces"@en . . "For a continuous map f : X -> X of a compact metric space, the set IR(f) of irregularly recurrent points is the set of points which are upper density recurrent, but not lower density recurrent. These notions are related to the structure of the measure center, but many problems still remain open. We solve some of them. The main result, based on examples by Obadalova and Smital [Obadalova L, Smltal J. Counterexamples to the open problem by Zhou and Feng on minimal center of attraction. Nonlinearity 2012;25:1443-9], shows that positive topological entropy supported by the center C-z of attraction of a point z is not related to the property that C-z is the support of an invariant measure generated by z. We also show that IR(f) is invariant with respect to standard operations, like f(IR(f)) = IR(f), or IR(f(m)) = IR(f) for m is an element of N." . "Irregular recurrence in compact metric spaces" . "Irregular recurrence in compact metric spaces"@en .