Snowflake Groups, Perron-frobenius Eigenvalues, and Isoperimetric Spectra

ar X iv : m at h / 06 08 15 5 v 1 [ m at h . G R ] 7 A ug 2 00 6 SNOWFLAKE GROUPS , PERRON - FROBENIUS EIGENVALUES , AND ISOPERIMETRIC SPECTRA

The k-dimensional Dehn (or isoperimetric) function of a group bounds the volume of efficient ball-fillings of k-spheres mapped into k-connected spaces on which the group acts properly and cocompactly; the bound is given as a function of the volume of the sphere. We advance significantly the observed range of behavior for such functions. First, to each non-negative integer matrix P and positive ...

Compact weighted Frobenius-Perron operators and their spectra

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.

ar X iv : m at h / 06 08 15 5 v 2 [ m at h . G R ] 1 7 Se p 20 08 Snowflake groups , Perron – Frobenius eigenvalues , and isoperimetric spectra

The k–dimensional Dehn (or isoperimetric) function of a group bounds the volume of efficient ball-fillings of k–spheres mapped into k–connected spaces on which the group acts properly and cocompactly; the bound is given as a function of the volume of the sphere. We advance significantly the observed range of behavior for such functions. First, to each non-negative integer matrix P and positive ...

Weighted Frobenius-Perron and Koopman operators

Spectrum Properties of the Koopman and Frobenius-Perron Operators