Ergodic Theory and Semisimple Groups

Zimmer, Robert J.

doi:10.1007/978-1-4684-9488-4

Cited by 827 publications

(883 citation statements)

References 0 publications

Supporting

Mentioning

847

Contrasting

Unclassified

Order By: Relevance

“…We will therefore content ourselves by exploring a dynamical view of this notion which has been exploited throughout the text. For further information, we refer the reader to [100,151,242,254].…”

Section: Figure 24mentioning

confidence: 99%

Groups of Circle Diffeomorphisms

Navas¹

2011

153

171

View full text Add to dashboard Cite

The original version (in Spanish) of this text was prepared for a mini-course in Antofagasta, Chile. Subsequently, enlarged and revised versions were published in the series Monografías del IMCA (Perú) and Ensaios Matemáticos (Brasil). This translation arose from the necessity of making this text accessible to a larger audience. I would like to thank Juan Rivera-Letelier for his invitation to the II Workshop on Dynamical Systems ( 2001), for which the original version was prepared, and Roger Metzger for his invitation to IMCA (2006), where part of this material was presented. I would also like to thank both Étienne Ghys and Maria Eulália Vares for motivating me and allowing me to publish the revised Spanish version in Brasil, as well as all the people who strongly encouraged me to conclude this English version.This work was partially supported by CONICYT and PBCT via the Research Network on Low Dimensional Dynamics. I would also to acknowledge the support of both the UMPA Department of the École Normale Supérieure de Lyon, where the idea of writing this text was born during my PhD thesis, and the Institut des Hautes Études Scientifiques, where the original notes started taking its definite form while I benefited from a one-year postdoctoral position.This work owes a lot to many of my colleges. Several remarks spread throughout the text and the content of some examples and exercises were born during fruitful and quite stimulating discussions. It is then a pleasure to thank Sylvain Crovisier (Proposition 4.2.25),

show abstract

Section: Figure 24mentioning

confidence: 99%

Groups of Circle Diffeomorphisms

Navas¹

2011

153

171

View full text Add to dashboard Cite

show abstract

“…But if this happens then the original cocycle is cohomologous to a cocycle taking values in the subgroup Z H φ . Remark: The subgroup Z H φ is algebraic, hence it contains the algebraic hull of the flow (see Feres [12], Zimmer [31]). …”

Section: Dynamics On Flag Bundles and Block Reductionmentioning

confidence: 99%

Morse and Lyapunov spectra and dynamics on flag bundles

Martín¹,

Seco²

2009

Ergod. Th. Dynam. Sys.

View full text Add to dashboard Cite

This paper studies characteristic exponents of flows in relation with the dynamics of flows on flag bundles. The starting point is a flow on a principal bundle with semi-simple group G. Projection against the Iwasawa decomposition G = KAN defines an additive cocycle over the flow with values in a = log A. Its Lyapunov exponents (limits along trajectories) and Morse exponents (limits along chains) are studied. It is proved a symmetric property of these spectral sets, namely invariance under the Weyl group. It is proved also that these sets are located in certain Weyl chambers, defined from the dynamics on the associated flag bundles. As a special case linear flows on vector bundles are considered.AMS 2000 subject classification: Primary: 37B05, 37B35. Secondary: 20M20, 22E46.

show abstract

“…The usual non-twisted cocycles, are known to show some rigidity on measurable ( [6]), C ∞ and Hölder ( [7], [5]) levels and to be highly unstable on continuous level. In sharp contrast to it, the non-trivially twisted cocycles show strong regularity already on the continuous level.…”

Section: Continuous Cocyclesmentioning

confidence: 99%

Untitled

Kononenko¹

1995

Electron. Res. Announc. Amer. Math. Soc.

View full text Add to dashboard Cite

Ergodic Theory and Semisimple Groups

Cited by 827 publications

References 0 publications

Groups of Circle Diffeomorphisms

Groups of Circle Diffeomorphisms

Morse and Lyapunov spectra and dynamics on flag bundles

Untitled

Contact Info

Product

Resources

About