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Rigidity in Dynamics and Geometry: Contributions from the Programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences Cambridge, United Kingdom, 5 January 7 July 2000 2002 ed. [Kõva köide]

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  • Formaat: Hardback, 492 pages, kõrgus x laius: 235x155 mm, kaal: 928 g, 8 Illustrations, black and white; XIII, 492 p. 8 illus., 1 Hardback
  • Ilmumisaeg: 13-May-2002
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540432434
  • ISBN-13: 9783540432432
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  • Formaat: Hardback, 492 pages, kõrgus x laius: 235x155 mm, kaal: 928 g, 8 Illustrations, black and white; XIII, 492 p. 8 illus., 1 Hardback
  • Ilmumisaeg: 13-May-2002
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540432434
  • ISBN-13: 9783540432432
Teised raamatud teemal:
This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from Jan­ uary until July, 2000. Beside the activities during the semester, there were workshops held in January, March and July, the first being of introductory nature with five short courses delivered over a week. Although the quality of the workshops was excellent throughout the semester, the idea of these proceedings came about during the March workshop, which is hence more prominently represented, The format of the volume has undergone many changes, but what has remained untouched is the enthusiasm of the contributors since the onset of the project: suffice it to say that even though only two months elapsed between the time we contacted the potential authors and the deadline to submit the papers, the deadline was respected in the vast majority of the cases. The scope of the papers is not completely uniform throughout the volume, although there are some points in common. We asked the authors to write papers keeping in mind the idea that they should be accessible to students. At the same time, we wanted the papers not to be a summary of results that appeared somewhere else.
Quasi-Conformal Geometry and Hyperbolic Geometry
1(18)
Marc Bourdon
Herve Pajot
Introduction
1(1)
Basic Tools in Geometric Function Theory and Quasi-Conformal Geometry
1(4)
Gromov Hyperbolic Groups: a Motivation for Quasi-Conformal Geometry
5(3)
Further Properties of Loewner Spaces and Spaces with Poincare Inequalities
8(3)
Differentiability of Quasi-Symmetric Homeomorphisms, Applications to Quasi-Isometry
11(8)
References
15(4)
On and Around the Bounded Cohomology of SL2
19(20)
Marc Burger
Nicolas Monod
Introduction
19(3)
Notations and Conventions
22(1)
A Differential Group
23(6)
Constructing Cocycles
29(4)
Above Degree Two
33(6)
References
36(3)
Density d'orbites d'actions de groupes lineaires et proprietes d'equidistribution de marches aleatoires
39(38)
Jean-Pierre Conze
Yves Guivarc'h
Introduction
39(2)
Ensemble limite, ensemble asymptotique
41(6)
Densite d'orbites de Γ dans LΓ (Rd) et equirepartition
47(12)
Actions sur les varietes de drapeaux homogenes
59(3)
La methode des equations fonctionnelles
62(6)
Actions des sous-groupes N et A sur Γ\G et Γ\G/M
68(9)
References
74(3)
Exceptional Sets in Dynamical Systems and Diophantine Approximation
77(22)
Maurice Dodson
Introduction
77(1)
Rotation Number
78(4)
Very Well Approximable Numbers and Khintchine's Theorem
82(2)
Kolmogorov-Arnol'd-Moser (KAM) Theory
84(3)
Linearisation
87(2)
Diophantine Approximation in Hyperbolic Geometry
89(4)
Extremal Manifolds and Flows
93(1)
Conclusion
94(5)
References
95(4)
An Introduction to Cocycle Super-Rigidity
99(36)
Renato Feres
Introduction
99(1)
Cocycles over Group Actions
100(5)
Cocycles and Principal Bundle Actions
105(8)
Semisimple Lie Groups, in a Hurry
113(4)
All the Ergodic Theory We Need
117(3)
The Algebraic Hull
120(3)
Super-Rigidity
123(1)
The Proof
124(7)
A Few Immediate Applications
131(4)
References
133(2)
Rigid Geometric Structures and Representations of Fundamental Groups
135(14)
David Fisher
Introduction
135(2)
Rigid Structures, Killing Fields and Representations of Fundamental Groups
137(2)
Representations of the Fundamental Group and Dynamics of the Action
139(4)
Constructing Quotients from Representations of π1
143(6)
References
146(3)
Coarse-Geometric Perspective on Negatively Curved Manifolds and Groups
149(18)
Alex Furman
Introduction
149(1)
The Geometric Setup
150(5)
Basic Notions of the Coarse-Geometric Setup
155(4)
Some Results
159(8)
References
165(2)
On Orbit Equivalence of Measure Preserving Actions
167(20)
Damien Gaboriau
Equivalence Relations
167(3)
Measure Equivalence
170(4)
Cost of an Equivalence Relation
174(3)
l2 Betti Numbers for Groups
177(3)
Simplicial Actions of an Equivalence Relation
180(2)
Actions of the Equivalence Relation on a Simplicial Complex
182(1)
l2 Betti Numbers for Equivalence Relations and Their Actions
183(4)
References
184(3)
The Margulis Invariant of Isometric Actions on Minkowski (2+1)-Space
187(16)
William M. Goldman
Introduction
187(1)
Affine Representations
188(2)
Lorentzian Geometry
190(1)
Deformation Theory
191(3)
Properness
194(1)
Linear Growth
195(1)
Triangle Group Deformations
196(7)
References
198(5)
Diophantine Approximation in Negatively Curved Manifolds and in the Heisenberg Group
203(24)
Sa'ar Hersonsky
Frederic Paulin
Introduction
203(1)
The Survey Part
204(9)
Diophantine Approximation in the Heisenberg Group
213(14)
References
225(2)
Appendix: Diophantine Approximation on Hyperbolic Surfaces
227(10)
Jouni Parkkonen
Frederic Paulin
References
236(1)
Bounded Cohomology, Boundary Maps, and Rigidity of Representations into Homeo+(S1) and SU(1, n)
237(24)
Alessandra Iozzi
Introduction
237(5)
The Euler Class and the Orientation Cocycle
242(1)
The Proof of the ``Formula''
243(5)
Γ-Equivalent Measurable Maps into M(S1)
248(3)
Semiconjugacy and the Proofs of Matsumoto's and Goldman's Theorems
251(10)
References
259(2)
SAT Actions and Ergodic Properties of the Horosphere Foliation
261(22)
Vadim A. Kaimanovich
Erdogic properties of SAT Actions
261(4)
The Horosphere Foliation and the Horocycle Flow
265(4)
Ergodicity of Busemann Cocycles
269(14)
References
280(3)
Nonexpanding Maps, Busemann Functions, and Multiplicative Ergodic Theory
283(12)
Anders Karlsson
Introduction
283(1)
Busemann Functions
284(1)
Subadditivity
285(1)
Nonexpanding Maps with Unbounded Orbit
286(2)
Multiplicative Ergodic Theory
288(3)
Nonexpansive Iterates in Banach Spaces
291(4)
References
292(3)
The Phase Space of k-Surfaces
295(14)
Francois Labourie
Presentation
295(1)
The Geodesic Flow
295(1)
One More Dimension
296(2)
A Hyperbolic Example
298(1)
Geometric Properties of k-Surfaces and Examples
298(2)
Phase Space
300(2)
Transversal Measure and Coding
302(3)
Questions
305(4)
References
307(2)
Schottky Subgroups of Mapping Class Groups and the Geometry of Surface-by-Free Groups
309(12)
Lee Mosher
Introduction
309(1)
Schottky Subgroups of Mapping Class Groups
310(3)
Geometry of Surface-by-Schottky Groups
313(3)
Stable Quasi-Geodesics in Teichmuller Space and the Ending Lamination Conjecture
316(5)
References
318(3)
Actions of Semisimple Lie Groups with Stationary Measure
321(24)
Amos Nevo
Robert J. Zimmer
Introduction
321(1)
Examples of Actions Without an Invariant Measure
322(1)
Stationary Measures
323(3)
A Structure Theorem for Stationary Measures
326(2)
Real Rank One Groups: Some Constructions
328(2)
Structure Theorems: Groups of Real Rank at Least Two
330(3)
Ergodicity Conditions and the Existence of Projective Factors of Full Entropy
333(5)
Construction of Projective Factors or Actions of Factor Groups
338(3)
Expanding Versus Contracting Automorphisms, and Margulis' Normal Subgroup Theorem
341(4)
References
342(3)
On the Cohomology of Anosov Actions
345(18)
Viorel Nitica
Andrei Torok
Cocycles
345(2)
Partially Hyperbolic and Anosov Actions
347(1)
Livsic Theory
348(3)
Regularity Results
351(2)
Higher Rank Abelian Actions
353(3)
Applications to the Rigidity of Higher Rank Lattice Actions
356(7)
References
359(4)
Harmonic Analysis and Hecke Operators
363(16)
Hee Oh
Uniform Pointwise Bounds ξs for Matrix Coefficients
363(4)
Equidistribution of Hecke Points
367(3)
Equidistribution of Integer Points on a Family of Homogeneous Varieties
370(4)
Distributing Points on the Spheres Sn (n ≥ 4)
374(5)
References
376(3)
Lp-Cohomology and Pinching
379(12)
Pierre Pansu
LP-Cohomology
381(2)
The Kunneth Formula
383(3)
Pinched Manifolds
386(1)
Non-Vanishing of Torsion
386(2)
Vanishing of Torsion for H2C
388(3)
References
388(3)
Classical and Non-Linearity Properties of Kac-Moody Lattices
391(16)
Bertrand Remy
Introduction
391(1)
A Classical Arithmetic Situation and its Geometric Formulation
392(3)
Kac-Moody Theory and the Generalization
395(5)
Questions Arising from the Generalization
400(7)
References
404(3)
Actions of Maximal Tori on Homogeneous Spaces
407(18)
George Tomarcov
Introduction
407(5)
K-Algebraic Groups, Arithmetic Subgroups and Central Simple Algebras
412(4)
Reductive Q-Subgroups of SL1(A)
416(3)
Homogeneous Orbit Closures Containing Relatively Compact T-Orbits
419(2)
Closed T-Orbits
421(4)
References
423(2)
Dynamics on Parameter Spaces: Submanifold and Fractal Subset Questions
425(16)
Barak Weiss
Introduction
425(2)
Conjectures and Results
427(2)
A Gentle Reminder Regarding Dynamics on Homogeneous / Quadratic Differential Spaces
429(3)
Quantitative Nondivergence and Applications
432(2)
Khinchin's Convergence Case for Fractals
434(3)
Logarithm Laws on a Teichmuller Horocycle
437(4)
References
439(2)
Superrigid Subgroups and Syndetic Hulls in Solvable Lie Groups
441(18)
Dave Witte
What Is a Superrigid Subgroup?
441(4)
Other Superrigidity Theorems
445(3)
Our Prototypical Proof of Superrigidity
448(4)
Solvable Lie Groups and Zariski Closed Subgroups
452(2)
Existence of Syndetic Hulls
454(5)
References
457(2)
Square Tiled Surfaces and Teichmuller Volumes of the Moduli Spaces of Abelian Differentials
459(14)
Anton Zorich
Motivations
459(1)
Translation Surfaces Versus Flat Surfaces
460(1)
Moduli Spaces of Abelian Differentials
461(1)
Counting Volume by Means of Counting Integer Points
462(1)
Two Examples of Computation
463(4)
Volumes of Some Strata of Abelian Differentials
467(1)
Lyapunov Exponents of the Teichmuller Geodesic Flow
467(2)
Conjectural Probability P(n) of n Bands of Trajectories for a Rational Interval Exchange Transformation
469(4)
References
471(2)
On Property (T) for Discrete Groups
473(10)
Andrzej Zuk
Introduction
473(1)
Expanders
474(2)
How to Prove Property (T)
476(2)
Random Groups
478(5)
References
480(3)
Index 483