Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure

Discrete and Continuous Dynamical Systems

Volumn 6, Issue 1, 2000, Pages 61-88

  Gunesch, Roland ^a   Katok, Anatole B ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Almost isometries; Conjugation approximation method; Measure preserving exponential map; Partition rearrangements; Weakly mixing diffeomorphisms

Indexed keywords

EID: 0034406172     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2000.6.61     Document Type: Article

References (17)

1. D.V. Anosov and A. Katok, New examples in smooth ergodic theory. Ergodic diffeomorphisms, Trans. Moscow Math. Soc., vol. 23 (1970).
2. R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Springer Lecture Notes in Mathematics, vol. 470 (1975)
3. R. Feres and A. Katok, Ergodic theory and dynamics of G-spaces (with a special emphasis on rigidity phenomena), Preprint (1999), to appear in "Handbook of dynamical systems", vol. 1, Elsevier (2000).
4. M. Gromov, Rigid transformation groups in Géometric différentielle, ed. D. Bernard and Y. Choquet-Bruhat, Travaux en cours, vol. 33, 65-139, Hermann, 1988.
5. B. Hasselblatt and A. Katok, Dynamical systems. Principal structures. Preprint, 1999, to appear in "Handbook in Dynamical Systems", vol. 1, Elsevier (2000).
6. B. Kalinin and A. Katok, Rigidity of invariant measures, factors and joinings for actions of higher-rank abelian groups, Preprint (1999).
7. A. Katok, S. Katok, and K. Schmidt, Rigidity of measurable structure for algebraic actions of higher-rank abelian groups, Preprint (1999).
8. A. Katok and R. Spatzier, Invariant measures for higher rank hyperbolic Abelian actions. Erg. Theory and Dynam. Systems, vol. 16 (1996), 751-778.
9. F. Ledrappier, Propriétés ergodiques des mesures de Sinaï, Publications Mathématiques de l'Institut des Hautes Études Scientifiques vol. 59 (1984) 163-188.
10. Ya. B. Pesin, Characteristic Lyapunov exponents and smooth ergodic theory, Russian Math Surveys, vol. 32 (1977), 55-114.
11. M. Ratner, Rigidity of horocycle flows, Ann. of Math. vol. 115 (1982), 597-614.
12. M. Ratner, Rigidity of time changes for horocycle flows, Acta Math. vol. 156 (1986), 1-32.
13. J.-C. Yoccoz, Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie, une condition Diophantienne, Ann. Sci. École Norm. Sup. vol. 17 (1984) 333-361.
14. R. Zimmer, Ergodic theory and semisimple groups, Birkhäuser, 1984.
15. R. Zimmer, Lattices in semisimple groups and invariant geometric structures on compact manifolds, Discrete groups in geometry and analysis (New Haven, Conn., 1984), 152-210, Progr. Math., 67, Birkhäuser Boston, Boston, Mass., 1987.
16. R. Zimmer, Lattices in semisimple groups and invariant geometric structures on compact manifolds, Discrete groups in geometry and analysis (New Haven, Conn., 1984), 152-210, Progr. Math., 67, Birkhäuser Boston, Boston, Mass., 1987.
17. R. Zimmer, Spectrum, entropy and geometric structures for smooth actions of Kazhdan groups Isr. Jour. Math., vol. 75 (1991), 65-80.