Abstract
Three different configurations of fold and flip bifurcation curves of maps, centered round a cusp point of a fold curve, are considered. They are called saddle area, spring area and crossroad area. For one and two-dimensional maps, this paper uses the notion of contour lines in a parameter plane. A given contour line is related to a constant value of a "reduced multiplier" constructed from the trace and the Jacobian of the matrix associated with a given periodic point. The singularities of such lines define the configuration type of the areas indicated above. When a third parameter varies, the qualitative changes of such areas are directly identified. These singularities also enable the determination of a point of intersection of two bifurcation curves of the same nature (flip or fold), and, when a third parameter varies, the appearance (or disappearance) of a closed fold or flip bifurcation curve.
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.
