Dynamical behavior of a parametrized family of one-dimensional maps

Mustu Erkan: Dynamical behavior of a parametrized family of one-dimensional maps. (2022)

[thumbnail of ejqtde_2022_025.pdf] Teljes mű

Download (816kB)


The connection of these maps to homoclinic loops acts like an amplifier of the map behavior, and makes it interesting also in the case where all map orbits approach zero (but in many possible ways). We introduce so-called ‘flat’ intervals containing exactly one maximum or minimum, and so-called ‘steep’ intervals containing exactly one zero point of fµ,ω and no zero of f 0 µ,ω. For specific parameters µ and ω, we construct an open set of points with orbits staying entirely in the ‘flat’ intervals in section three. In section four, we describe orbits staying in the ‘steep’ intervals (for open parameter sets), and in section five (for specific parameters) orbits regularly changing between ‘steep’ and ‘flat’ intervals. Both orbit types are described by symbol sequences, and it is shown that their Lebesgue measure is zero.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2022
Number: 25
ISSN: 1417-3875
Number of Pages: 35
Language: English
Place of Publication: Szeged
DOI: 10.14232/ejqtde.2022.1.25
Uncontrolled Keywords: Differenciálegyenlet
Additional Information: Bibliogr.: 35. p. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
Date Deposited: 2022. Sep. 08. 14:48
Last Modified: 2022. Nov. 08. 08:33
URI: http://acta.bibl.u-szeged.hu/id/eprint/76526

Actions (login required)

View Item View Item