Coxeter groups, Salem numbers and the Hilbert metric
By Curtis T. McMullen. 2002
92 citations recorded by the source corpus.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/11f5f5a55d6c50ee90b5ea94e9aa8a058dcd35c3
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In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
Citations in the corpus
- On groups generated by two positive multi-twists: Teichmuller curves and Lehmer's number (2003, methodology): “the analysis of the curve configurations and prove Theorem 1.3. This leads us to §9 where we relate information about certain 2-twist groups to data from associated Coxeter groups using the results of [37], and to the monodromy of associated fibered links in S3 (see [23]). In §10 we provide a few appl”
- Around groups in Hilbert Geometry (2013, background): “ft to the reader: Lemma 2.7. Let 2Aut( ;H;p). If ˆ+ = 1 then h( ) = 0 and preserves all the algebraic horospheres based at (H;p) of . If ˆ+ >1 then h( ) 6= 0 . Lemma 2.8. [McMullen, Theorem 2.1 of [64]] Let 2Aut( ). The translation length satises: 1 2 lnmax(ˆ+ ;1=ˆ ;ˆ + =ˆ ) 6 ˝ ( ) 6 lnmax(ˆ+ ;1”
- Dynamical degrees of birational transformations of projective surfaces (2013, background): “More precisely, McMullen proves that there are Salem numbers between λL and λP which are not realized by eigenvalues of elements in the Coxeter groups Wn (see [36]), and we deduce from this that there are Salem numbers which are not realized by dynamical degrees of automorphisms of surfaces (see [37”
- Dynamics on blowups of the projective plane (2007, unknown): “is a Coxeter group, we have σ(w) ≥ λLehmer by [ Mc1 ], completing the proof.”
- The Geometry and Topology of Coxeter Groups (2025, methodology): “(However, in [200] McMullen makes effective use of a “Hilbert metric” on I.”
- Dynamics of automorphisms on projective complex manifolds (2008, background): “These notions might be the geometrical incarnations of McMullen’s lattice-theoretical notion ”essential lattice isometry” in [ 35 ] §4. By the way, all surface automorphisms of positive entropy are automatically primitive.”