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Volumn 9, Issue 13, 2003, Pages 99-110

Rigidity properties of ℤd-actions on tori and solenoids

Author keywords

Entropy; Invariant measures; Invariant algebras; Joinings; Measurable factors; Solenoid automorphism; Toral automorphisms

Indexed keywords


EID: 15944420582     PISSN: None     EISSN: 10796762     Source Type: Journal    
DOI: 10.1090/S1079-6762-03-00117-3     Document Type: Article
Times cited : (33)

References (27)
  • 1
    • 84967780444 scopus 로고
    • Multi-invariant sets on tori
    • MR 85b:11064
    • Daniel Berend, Multi-invariant sets on tori, Trans. Amer. Math. Soc. 280 (1983), no. 2, 509-532. MR 85b:11064
    • (1983) Trans. Amer. Math. Soc , vol.280 , Issue.2 , pp. 509-532
    • Berend, D.1
  • 2
    • 2642530136 scopus 로고
    • Multi-invariant sets on compact abelian groups
    • MR 86e:22009
    • Daniel Berend, Multi-invariant sets on compact abelian groups, Trans. Amer. Math. Soc. 286 (1984), no. 2, 505-535. MR 86e:22009
    • (1984) Trans. Amer. Math. Soc. , vol.286 , Issue.2 , pp. 505-535
    • Berend, D.1
  • 3
    • 0038675079 scopus 로고    scopus 로고
    • Invariant measures on G\Γ for split simple Lie groups G
    • Manfred Einsiedler and Anatole Katok, Invariant measures on G\Γ for split simple Lie groups G, Comm. Pure Appl. Math. 56 (2003), no. 8, 1184-1221.
    • (2003) Comm. Pure Appl. Math , vol.56 , Issue.8 , pp. 1184-1221
    • Einsiedler, M.1    Katok, A.2
  • 6
    • 14644399109 scopus 로고    scopus 로고
    • Irreducibility, homoclinic points and adjoint actions of algebraic ℤ-actions of rank one, Dynamics and randomness (Santiago, 2000)
    • d-actions of rank one, Dynamics and randomness (Santiago, 2000), Nonlinear Phenom. Complex Systems 7 (2002), 95-124.
    • Nonlinear Phenom. Complex Systems , vol.7 , Issue.2002 , pp. 95-124
    • Einsiedler, M.1    Schmidt, K.2
  • 7
    • 51249170411 scopus 로고
    • A generalization of a result of R. Lyons about measures on [0; 1), Israel
    • MR 95f:28020
    • J. Feldman, A generalization of a result of R. Lyons about measures on [0; 1), Israel J. Math. 81 (1993), no. 3, 281-287. MR 95f:28020
    • (1993) J. Math , vol.81 , Issue.3 , pp. 281-287
    • Feldman, J.1
  • 8
    • 33646727744 scopus 로고
    • Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation
    • MR 35:4369
    • Harry Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Systems Theory 1 (1967), 1-49. MR 35:4369
    • (1967) Math. Systems Theory , vol.1 , pp. 1-49
    • Furstenberg, H.1
  • 9
    • 0030444048 scopus 로고
    • Nombres normaux, entropie, translations
    • MR 96g:11092
    • Bernard Host, Nombres normaux, entropie, translations, Israel J. Math. 91 (1995), no. 1-3, 419-428. MR 96g:11092
    • (1995) Israel J. Math , vol.91 , Issue.1-3 , pp. 419-428
    • Host, B.1
  • 10
    • 78149345672 scopus 로고
    • Some ergodic properties of commuting Diffeomorphisms, Ergodic Theory Dynam
    • MR 94b:58061
    • Hu Yi Hu, Some ergodic properties of commuting Diffeomorphisms, Ergodic Theory Dynam. Systems 13 (1993), no. 1, 73-100. MR 94b:58061
    • (1993) Systems , vol.13 , Issue.1 , pp. 73-100
    • Hu Yi, H.1
  • 11
    • 51249165880 scopus 로고
    • Measures on the circle invariant under multiplication by a nonlacunary subsemigroup of the integers
    • MR 93m:28019
    • Aimee S. A. Johnson, Measures on the circle invariant under multiplication by a nonlacunary subsemigroup of the integers, Israel J. Math. 77 (1992), no. 1-2, 211-240. MR 93m:28019
    • (1992) Israel J. Math , vol.77 , Issue.1-2 , pp. 211-240
    • Johnson, A.S.A.1
  • 13
    • 0005422062 scopus 로고    scopus 로고
    • Invariant measures for actions of higher rank abelian groups, Smooth ergodic theory and its applications (Seattle, WA, 1999)
    • Amer. Math. Soc., Providence, RI, MR 2002i:37035
    • Boris Kalinin and Anatole Katok, Invariant measures for actions of higher rank abelian groups, Smooth ergodic theory and its applications (Seattle, WA, 1999), Proc. Sympos. Pure Math., vol. 69, Amer. Math. Soc., Providence, RI, 2001, pp. 593-637. MR 2002i:37035
    • (2001) Proc. Sympos. Pure Math , vol.69 , pp. 593-637
    • Kalinin, B.1    Katok, A.2
  • 14
    • 0036052317 scopus 로고    scopus 로고
    • Measurable rigidity and disjointness for Zk actions by toral automorphisms
    • Boris Kalinin and Anatole Katok, Measurable rigidity and disjointness for Zk actions by toral automorphisms, Ergodic Theory Dynam. Systems 22 (2002), no. 2, 507-523.
    • (2002) Ergodic Theory Dynam. Systems , vol.22 , Issue.2 , pp. 507-523
    • Kalinin, B.1    Katok, A.2
  • 15
    • 0036951258 scopus 로고    scopus 로고
    • Rigidity of measurable structure for Zdactions by automorphisms of a torus
    • MR 2003h:37007
    • Anatole Katok, Svetlana Katok, and Klaus Schmidt, Rigidity of measurable structure for Zdactions by automorphisms of a torus, Comment. Math. Helv. 77 (2002), no. 4, 718-745. MR 2003h:37007
    • (2002) Comment. Math. Helv , vol.77 , Issue.4 , pp. 718-745
    • Katok, A.1    Katok, S.2    Schmidt, K.3
  • 16
    • 0030520144 scopus 로고    scopus 로고
    • Invariant measures for higher-rank hyperbolic abelian actions, Ergodic Theory Dynam
    • MR 97d:58116
    • A. Katok and R. J. Spatzier, Invariant measures for higher-rank hyperbolic abelian actions, Ergodic Theory Dynam. Systems 16 (1996), no. 4, 751-778. MR 97d:58116
    • (1996) Systems , vol.16 , Issue.4 , pp. 751-778
    • Katok, A.1    Spatzier, R.J.2
  • 17
    • 0030520144 scopus 로고    scopus 로고
    • Corrections to: "Invariant measures for higher-rank hyperbolic abelian actions
    • MR 97d:58116]
    • A. Katok and R. J. Spatzier, Corrections to: "Invariant measures for higher-rank hyperbolic abelian actions" [Ergodic Theory Dynam. Systems 16 (1996), no. 4, 751-778; MR 97d:58116]
    • (1996) Ergodic Theory Dynam. Systems , vol.16 , Issue.4 , pp. 751-778
    • Katok, A.1    Spatzier, R.J.2
  • 18
    • 0345914003 scopus 로고    scopus 로고
    • MR 99c:58093
    • Ergodic Theory Dynam. Systems 18 (1998), no. 2, 503-507. MR 99c:58093
    • (1998) Ergodic Theory Dynam. Systems , vol.18 , Issue.2 , pp. 503-507
  • 19
    • 0001048955 scopus 로고
    • The metric entropy of Diffeomorphisms. I. Characterization of measures satisfying Pesin's entropy formula
    • MR 87i:58101a
    • F. Ledrappier and L.-S. Young, The metric entropy of Diffeomorphisms. I. Characterization of measures satisfying Pesin's entropy formula, Ann. of Math. (2) 122 (1985), no. 3, 509-539. MR 87i:58101a
    • (1985) Ann. Of Math. (2) , vol.122 , Issue.3 , pp. 509-539
    • Ledrappier, F.1    Young, L.-S.2
  • 20
    • 0001048955 scopus 로고
    • The metric entropy of Diffeomorphisms. II. Relations between entropy, exponents and dimension
    • MR 87i:58101b
    • F. Ledrappier and L.-S. Young, The metric entropy of Diffeomorphisms. II. Relations between entropy, exponents and dimension, Ann. of Math. (2) 122 (1985), no. 3, 540-574. MR 87i:58101b
    • (1985) Ann. Of Math. (2) , vol.122 , Issue.3 , pp. 540-574
    • Ledrappier, F.1    Young, L.-S.2
  • 21
    • 0035648687 scopus 로고    scopus 로고
    • P-adic foliation and equidistribution
    • MR 2002c:28031
    • Elon Lindenstrauss, p-adic foliation and equidistribution, Israel J. Math. 122 (2001), 29-42. MR 2002c:28031
    • (2001) Israel J. Math , vol.122 , pp. 29-42
    • Lindenstrauss, E.1
  • 23
    • 0033444772 scopus 로고    scopus 로고
    • Entropy of convolutions on the circle
    • MR 2001a:28019
    • Elon Lindenstrauss, David Meiri, and Yuval Peres, Entropy of convolutions on the circle, Ann. of Math. (2) 149 (1999), no. 3, 871-904. MR 2001a:28019
    • (1999) Ann. Of Math. (2) , vol.149 , Issue.3 , pp. 871-904
    • Lindenstrauss, E.1    Meiri, D.2    Peres, Y.3
  • 24
    • 51249178044 scopus 로고
    • On measures simultaneously 2- and 3-invariant
    • MR 89e:28031
    • Russell Lyons, On measures simultaneously 2- and 3-invariant, Israel J. Math. 61 (1988), no. 2, 219-224. MR 89e:28031
    • (1988) Israel J. Math , vol.61 , Issue.2 , pp. 219-224
    • Lyons, R.1
  • 25
    • 0039180523 scopus 로고    scopus 로고
    • Squaring and cubing the circle Rudolph's theorem, Ergodic theory of Zd actions (Warwick, 1993-1994)
    • Cambridge Univ. Press, Cambridge, MR 97h:28009
    • William Parry, Squaring and cubing the circle Rudolph's theorem, Ergodic theory of Zd actions (Warwick, 1993-1994), London Math. Soc. Lecture Note Ser., vol. 228, Cambridge Univ. Press, Cambridge, 1996, pp. 177-183. MR 97h:28009
    • (1996) London Math. Soc. Lecture Note Ser , vol.228 , pp. 177-183
    • Parry, W.1
  • 26
    • 84972113917 scopus 로고
    • Rudolph, ×2 and ×3 invariant measures and entropy, Ergodic Theory Dynam
    • MR 91g:28026
    • Daniel J. Rudolph, ×2 and ×3 invariant measures and entropy, Ergodic Theory Dynam. Systems 10 (1990), no. 2, 395-406. MR 91g:28026
    • (1990) Systems , vol.10 , Issue.2 , pp. 395-406
    • Daniel, J.1
  • 27
    • 0003251283 scopus 로고
    • Dynamical systems of algebraic origin
    • Birkhäuser Verlag, Basel, MR 97c:28041
    • Klaus Schmidt, Dynamical systems of algebraic origin, Progress in Mathematics, vol. 128, Birkhäuser Verlag, Basel, 1995. MR 97c:28041
    • (1995) Progress in Mathematics , vol.128
    • Schmidt, K.1


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