Groups of circle diffeomorphisms / Andrés Navas
- Author:
- Navas, Andrés
- Published:
- Chicago : University of Chicago Press, 2011.
- Physical Description:
- xviii, 290 pages : illustrations ; 24 cm.
- Series:
- Chicago lectures in mathematics series
- Contents:
- Machine generated contents note: 1.Examples of Group Actions on the Circle -- 1.1.The Group of Rotations -- 1.2.The Group of Translations and the Affine Group -- 1.3.The Group PSL(2, R) -- 1.3.1.PSL(2, R) as the Mobius group -- 1.3.2.PSL(2, R) and the Liouville geodesic current -- 1.3.3.PSL(2, R) and the convergence property -- 1.4.Actions of Lie Groups -- 1.5.Thompson's Groups -- 1.5.1.Thurston's piecewise projective realization -- 1.5.2.Ghys-Sergiescu's smooth realization -- 2.Dynamics of Groups of Homeomorphisms -- 2.1.Minimal Invariant Sets -- 2.1.1.The case of the circle -- 2.1.2.The case of the real line -- 2.2.Some Combinatorial Results -- 2.2.1.Poincare's theory -- 2.2.2.Rotation numbers and invariant measures -- 2.2.3.Faithful actions on the line -- 2.2.4.Free actions and Holder's theorem -- 2.2.5.Translation numbers and quasi-invariant measures -- 2.2.6.An application to amenable, orderable groups -- 2.3.Invariant Measures and Free Groups -- 2.3.1.A weak version of the Tits alternative -- 2.3.2.A probabilistic viewpoint -- 3.Dynamics of Groups of Diffeomorphisms -- 3.1.Denjoy's Theorem -- 3.2.Sacksteder's Theorem -- 3.2.1.The classical version in class C1+LiP -- 3.2.2.The C1 version for pseudogroups -- 3.2.3.A sharp C1 version via Lyapunov exponents -- 3.3.Dummy's First Theorem: On the Existence of Exceptional Minimal Sets -- 3.3.1.The statement of the result -- 3.3.2.An expanding first-return map -- 3.3.3.Proof of the theorem -- 3.4.Dummy's Second Theorem: On the Space of Semiexceptional Orbits -- 3.4.1.The statement of the result -- 3.4.2.A criterion for distinguishing two different ends -- 3.4.3.End of the proof -- 3.5.Two Open Problems -- 3.5.1.Minimal actions -- 3.5.2.Actions with an exceptional minimal set -- 3.6.On the Smoothness of the Conjugacy between Groups of Diffeomorphisms -- 3.6.1.Sternberg's linearization theorem and C1 conjugacies -- 3.6.2.The case of bi-Lipschitz conjugacies -- 4.Structure and Rigidity via Dynamical Methods -- 4.1.Abelian Groups of Diffeomorphisms -- 4.1.1.Kopell's lemma -- 4.1.2.Classifying Abelian group actions in class C2 -- 4.1.3.Szekeres's theorem -- 4.1.4.Denjoy counterexamples -- 4.1.5.On intermediate regularities -- 4.2.Nilpotent Groups of Diffeomorphisms -- 4.2.1.The Plante-Thurston Theorems -- 4.2.2.On growth of groups of diffeomorphisms -- 4.2.3.Nilpotence, growth, and intermediate regularity -- 4.3.Polycyclic Groups of Diffeomorphisms -- 4.4.Solvable Groups of Diffeomorphisms -- 4.4.1.Some examples and statements of results -- 4.4.2.The metabelian case -- 4.4.3.The case of the real line -- 4.5.On the Smooth Actions of Amenable Groups -- 5.Rigidity via Cohomological Methods -- 5.1.Thurston's Stability Theorem -- 5.2.Rigidity for Groups with Kazhdan's Property (T) -- 5.2.1.Kazhdan's property (T) -- 5.2.2.The statement of the result -- 5.2.3.Proof of the theorem -- 5.2.4.Relative property (T) and Haagerup's property -- 5.3.Superrigidity for Higher-Rank Lattice Actions -- 5.3.1.Statement of the result -- 5.3.2.Cohomological superrigidity -- 5.3.3.Superrigidity for actions on the circle.
- Subject(s):
- ISBN:
- 9780226569512 (cloth : alk. paper)
0226569519 (cloth : alk. paper) - Bibliography Note:
- Includes bibliographical references (pages [273]-286) and index.
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