Abstract
The structure of the phase-locked zones in the sine map is examined. Attention is drawn to general features of the map's phase diagram and two, dynamically distinct kinds of bistability are distinguished: One type arises locally through a cusp catastrophe and the other, nonlocally, through crossing (in the parameter plane) of remote stable manifolds. Numerical work indicates that a Cantor set of cusp bistabilities and other related features forms an infinite binary tree in every Arnol'd tongue. (An infinite set of such structures lies arbitrarily close to the parameter line for the quasiperiodic transition to chaos, and also appears in other phase-locked zones.) The binary tree of features obeys the vector scaling found in the quartic map and seems to be generic for multiple-extrema, one-dimensional maps.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
