Abstract
A sharp bound on the number of invariant components of an interval exchange transformation (IET) is provided. More precisely, it is proved that the number of periodic components nper and the number of minimal components nmin of an interval exchange transformation of n intervals satisfy nper + 2 nmin ⩽ n. Moreover, it is shown that almost all IETs are typical, that is, all have stable periodic components and all the minimal components are robust (i.e. persistent under almost all small perturbations). Finally, we find all the possible values for the integer vector (nper, nmin) for all typical IET of n intervals.
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.
