TY - JOUR
T1 - Attractors from one dimensional lorenz-like maps
AU - Choi, Youngna
PY - 2004
Y1 - 2004
N2 - In this paper we study the properties of expanding maps with a single discontinuity on a closed interval and the resultant dynamics. For such a map, there exists a compact invariant subset which shares a lot of common properties with classical attractors such as the topological transitivity of the restricted map and the density of the periodic points. The invariant set, with more conditions on the boundary, can be shown to have an isolating neighborhood, hence is a chaotic attractor in the strong sense. Not all such maps derive trapping regions, yet by perturbation, those non-attractors can be made to have a trapping region.
AB - In this paper we study the properties of expanding maps with a single discontinuity on a closed interval and the resultant dynamics. For such a map, there exists a compact invariant subset which shares a lot of common properties with classical attractors such as the topological transitivity of the restricted map and the density of the periodic points. The invariant set, with more conditions on the boundary, can be shown to have an isolating neighborhood, hence is a chaotic attractor in the strong sense. Not all such maps derive trapping regions, yet by perturbation, those non-attractors can be made to have a trapping region.
KW - Attractors
KW - Expanding maps
KW - Invariant sets
UR - http://www.scopus.com/inward/record.url?scp=4944254474&partnerID=8YFLogxK
U2 - 10.3934/dcds.2004.11.715
DO - 10.3934/dcds.2004.11.715
M3 - Article
AN - SCOPUS:4944254474
SN - 1078-0947
VL - 11
SP - 715
EP - 730
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 2-3
ER -