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Generalized northsouth dynamics on the space of geodesic currents
, 2014
"... We prove uniform northsouth dynamics type results for the action of ϕ ∈ Out(FN) on the space of projectivized geodesic currents PCurr(S) = PCurr(FN), where ϕ is induced by a pseudoAnosov homeomorphism on a compact surface S with boundary such that pi1(S) = FN. As an application, we show that f ..."
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Cited by 2 (1 self)
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We prove uniform northsouth dynamics type results for the action of ϕ ∈ Out(FN) on the space of projectivized geodesic currents PCurr(S) = PCurr(FN), where ϕ is induced by a pseudoAnosov homeomorphism on a compact surface S with boundary such that pi1(S) = FN. As an application, we show
The actions of Out(Fk) on the boundary of outer space and on the space of currents: minimal sets and equivariant incompatibility
, 2006
"... We prove that for k ≥ 5 there does not exist a continuous map ∂CV (Fk) → PCurr(Fk) that is either Out(Fk)equivariant or Out(Fk)antiequivariant. Here ∂CV (Fk) is the “lengthfunction” boundary of CullerVogtmann’s Outer space CV (Fk), and PCurr(Fk) is the space of projectivized geodesic currents ..."
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Cited by 25 (14 self)
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We prove that for k ≥ 5 there does not exist a continuous map ∂CV (Fk) → PCurr(Fk) that is either Out(Fk)equivariant or Out(Fk)antiequivariant. Here ∂CV (Fk) is the “lengthfunction” boundary of CullerVogtmann’s Outer space CV (Fk), and PCurr(Fk) is the space of projectivized geodesic currents
geodesic
"... Improved morphological interpolation of elevation contour data with generalised ..."
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Improved morphological interpolation of elevation contour data with generalised
The PattersonSullivan embedding and minimal volume entropy for Outer space
 Geom. Funct. Anal. (GAFA
"... Abstract. Motivated by Bonahon’s result for hyperbolic surfaces, we construct an analogue of the PattersonSullivanBowenMargulis map from the CullerVogtmann outer space CV (Fk) into the space of projectivized geodesic currents on a free group. We prove that this map is a topological embedding and ..."
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Cited by 21 (14 self)
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Abstract. Motivated by Bonahon’s result for hyperbolic surfaces, we construct an analogue of the PattersonSullivanBowenMargulis map from the CullerVogtmann outer space CV (Fk) into the space of projectivized geodesic currents on a free group. We prove that this map is a topological embedding
Hyperbolic structures on surfaces and geodesic currents
, 2014
"... These are lecture notes for a course given by the authors during the program Automorphisms of Free Groups: Geometry, Topology, and Dynamics, held at the CRM (Barcelona) in 2012. The main objective of the notes is to describe Bonahon’s construction of Thurston’s compactification of Teichmüller spac ..."
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space, in terms of geodesic currents on surfaces. In the final section, we present several extensions of the notion of geodesic current to various other more general settings. 1
Geometric entropy of geodesic currents on free groups
 Dynamical Numbers: Interplay Between Dynamical Systems and Number Theory, Contemporary Mathematics series, American Mathematical Society
"... Abstract. A geodesic current on a free group F is an Finvariant measure on the set ∂ 2 F of pairs of distinct points of ∂F. The space of geodesic currents on F is a natural companion of CullerVogtmann’s Outer space cv(F) and studying them together yields new information about both spaces as well a ..."
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Cited by 4 (3 self)
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(T) and the extremal distortion of distances in T with respect to distances in T ′. It follows that, given T in the projectivized outer space CV (F), h T ′(µT) as function of T ′ ∈ CV (F) achieves a strict global maximum at T ′ = T. We also show that for any T ∈ cv(F) and any geodesic current µ on F, hT (µ) ≤ h
c © Birkhäuser Verlag, Basel 2007 GAFA Geometric And Functional Analysis THE PATTERSON–SULLIVAN EMBEDDING AND MINIMAL VOLUME ENTROPY FOR OUTER SPACE
"... Abstract. Motivated by Bonahon’s result for hyperbolic surfaces, we construct an analogue of the Patterson–Sullivan–Bowen–Margulis map from the Culler–Vogtmann outer space CV (Fk) into the space of projectivized geodesic currents on a free group. We prove that this map is a continuous embedding an ..."
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Abstract. Motivated by Bonahon’s result for hyperbolic surfaces, we construct an analogue of the Patterson–Sullivan–Bowen–Margulis map from the Culler–Vogtmann outer space CV (Fk) into the space of projectivized geodesic currents on a free group. We prove that this map is a continuous embedding
Introduction Finsler Geometry of Projectivized Vector Bundles
, 2003
"... The purpose of this article is to reformulate the algebraic geometric concept of ..."
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Cited by 3 (0 self)
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The purpose of this article is to reformulate the algebraic geometric concept of
Geodesic Patterns
"... Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which d ..."
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Cited by 16 (6 self)
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Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which
Results 1  10
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25,843