TY - JOUR
T1 - Cubic maps as models of two-dimensional antimonotonicity
AU - Dawson, Silvina Ponce
AU - Grebogi, Celso
PY - 1991
Y1 - 1991
N2 - Families of dissipative two-dimensional diffeomorphisms that satisfy certain regularity conditions have been proved to be antimonotone [Kan et al., preprint (1990)], i.e. there are infinitely many periodic orbits created and infinitely many destroyed near certain parameter values of the system. We show that, in general, this sequence of creation and destruction of periodic orbits can also be modeled by families of one-dimensional maps with at least two critical points.
AB - Families of dissipative two-dimensional diffeomorphisms that satisfy certain regularity conditions have been proved to be antimonotone [Kan et al., preprint (1990)], i.e. there are infinitely many periodic orbits created and infinitely many destroyed near certain parameter values of the system. We show that, in general, this sequence of creation and destruction of periodic orbits can also be modeled by families of one-dimensional maps with at least two critical points.
UR - http://www.scopus.com/inward/record.url?scp=0000734928&partnerID=8YFLogxK
U2 - 10.1016/0960-0779(91)90004-S
DO - 10.1016/0960-0779(91)90004-S
M3 - Article
AN - SCOPUS:0000734928
SN - 0960-0779
VL - 1
SP - 137
EP - 144
JO - Chaos, Solitons & Fractals
JF - Chaos, Solitons & Fractals
IS - 2
ER -