TY - JOUR
T1 - Geometric mechanism for antimonotonicity in scalar maps with two critical points
AU - Dawson, Silvina Ponce
AU - Grebogi, Celso
AU - Koçak, Hüseyin
PY - 1993/9/1
Y1 - 1993/9/1
N2 - Concurrent creation and destruction of periodic orbits-antimonotonicity-for one-parameter scalar maps with at least two critical points are investigated. It is observed that if, for a parameter value, two critical points lie in an interval that is a chaotic attractor, then, generically, as the parameter is varied through any neighborhood of such a value, periodic orbits should be created and destroyed infinitely often. A general mechanism for this complicated dynamics for one-dimensional multimodal maps is proposed similar to the one of contact-making and contact-breaking homoclinic tangencies in two-dimensional dissipative maps. This subtle phenomenon is demonstrated in a detailed numerical study of a specific one-dimensional cubic map.
AB - Concurrent creation and destruction of periodic orbits-antimonotonicity-for one-parameter scalar maps with at least two critical points are investigated. It is observed that if, for a parameter value, two critical points lie in an interval that is a chaotic attractor, then, generically, as the parameter is varied through any neighborhood of such a value, periodic orbits should be created and destroyed infinitely often. A general mechanism for this complicated dynamics for one-dimensional multimodal maps is proposed similar to the one of contact-making and contact-breaking homoclinic tangencies in two-dimensional dissipative maps. This subtle phenomenon is demonstrated in a detailed numerical study of a specific one-dimensional cubic map.
UR - http://www.scopus.com/inward/record.url?scp=4244059264&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.48.1676
DO - 10.1103/PhysRevE.48.1676
M3 - Article
AN - SCOPUS:4244059264
SN - 1063-651X
VL - 48
SP - 1676
EP - 1682
JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 3
ER -