The problem of description of the set Per(f) of all minimal periods of a self-map f:X → X is studied. If X is a rational exterior space (e.g. a compact Lie group) then there exists a description of the set of minimal periods analogous to that for a torus map given by Jiang and Llibre. Our approach is based on the Haibao formula for the Lefschetz number of a self-map of a rational exterior space.
Let f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[f] which is equal to the...
Let f be a smooth self-map of an m-dimensional (m ≥ 4) closed connected and simply-connected manifold such that the sequence of the Lefschetz numbers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defined in combinatorial terms and is constant for all sufficiently large r. We compute J[f] for self-maps...
Let f be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension m ≥ 3 and r a fixed natural number. A topological invariant , introduced by the authors [Forum Math. 21 (2009)], is equal to the minimal number of r-periodic points for all smooth maps homotopic to f. In this paper we calculate for all self-maps of S³.
Abstract. Center of Applied Mathematics is the project co-financed by EuropeanUnion within the Human Capital Operational Programme. Its main aim is to promoteinterdisciplinary cooperation between mathematicians and the representativesof other disciplines as well as the development of the mathematical methods whichcould be useful in the sphere of applications. The project is realized at Faculty ofApplied Physics and Mathematics of Gdansk University o Technology. In the articlethe main tasks realized...
Healthy human heart rate is characterized by oscillations observed in intervals between consecutive heartbeats (RR intervals). Conventional methods of heart rate variability analysis measure the overall magnitude of RR interval fluctuations around its mean value or the magnitude of fluctuations in predetermined frequencies. The new methods of chaos theory and nonlinear dynamics provide powerful tools, which allow to predict clinical outcome in patients with cardiovascular diseases. The main aim...
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