Abstract
UDC 517.9 This descriptive text is essentially based on the Sharkovsky's and Myrberg's publications on the ordering of periodic solutions (<em>cycles</em>) generated by a D i m 1 unimodal smooth map f ( x , λ ) . Taking as an example f ( x , λ ) = x 2 - λ , it was shown in a paper published in1975 that the bifurcations are organized in the form of a sequence of <em>well-defined fractal embedded</em> ``<em>boxes</em>'' (parameter λ intervals), each of which is associated with a basic cycle of period k and a symbol j permitting to distinguish cycles with the same period k . Without using the denominations <em>Intermittency</em> (1980) and <em>Attractors in Crisis</em> (1982), this new text shows that the notion of <em>fractal embedded</em> ``<em>boxes</em>'' describes the properties of each of these two situations as the <em>limit of a sequence of well-defined boxes</em> ( k , j ) as k → ∞ .
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 callSimilar Papers
Disclaimer: 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.
