Mathematics – Geometric Topology
Scientific paper
2011-04-13
Mathematics
Geometric Topology
16 pages
Scientific paper
A pseudo-Anosov surface automorphism $\phi$ has associated to it an algebraic unit $\lambda_\phi$ called the dilatation of $\phi$. It is known that in many cases $\lambda_\phi$ appears as the spectral radius of a Perron-Frobenius matrix preserving a symplectic form $L$. We investigate what algebraic units could potentially appear as dilatations by first showing that every algebraic unit $\lambda$ appears as an eigenvalue for some integral symplectic matrix. We then show that if $\lambda$ is real and the greatest in modulus of its algebraic conjugates and their inverses, then $\lambda^n$ is the spectral radius of an integral Perron-Frobenius matrix preserving a prescribed symplectic form $L$. An immediate application of this is that for $\lambda$ as above, $\log(\lambda^n)$ is the topological entropy of a subshift of finite type.
No associations
LandOfFree
Achievable spectral radii of symplectic Perron-Frobenius matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Achievable spectral radii of symplectic Perron-Frobenius matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Achievable spectral radii of symplectic Perron-Frobenius matrices will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-164869