Abstract
We consider the space Ω of colored tilings corresponding to a weighted substitution introduced by one of the authors in [1], which is a kind of natural extension of the f-expansion for a piecewise linar f. We give a characterization of adapted coboundaries, which are α- G-homogeneous on the space of integer points Ω 0 , where α is a complex number with a negative real part. The image of such a coboundary corresponding to a weighted substitution of cubic Pisot type, is a fractal set called Rauzy fractal. We also consider the Fibonacci tiling and the α- G-homogeneous, adapted coboundary on it. This coboundary together with the fractional part give a geometrical representation of the Fibonacci expansions that is more or less known.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.