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Weak mixing suspension flows over shifts of finite type are universal
1. | Department of Mathematics and Statistics, University of Victoria, P.O. Box 3060 STN CSC, Victoria, B.C., V8W 3R4 |
2. | Department of Mathematics and Statistics, University of Victoria, PO BOX 3060 STN CSC, Victoria, BC V8W 3R4, Canada |
References:
[1] |
S. Alpern, Generic properties of measure preserving homeomorphisms,, In, 729 (1979), 16.
|
[2] |
A. Bellow and H. Furstenberg, An application of number theory to ergodic theory and the construction of uniquely ergodic models. A collection of invited papers on ergodic theory,, Israel J. Math., 33 (1979), 231.
doi: 10.1007/BF02762163. |
[3] |
R. Bowen, The equidistribution of closed geodesics,, Amer. J. Math., 94 (1972), 413.
|
[4] |
R. Bowen, One-dimensional hyperbolic sets for flows,, J. Differential Equations, 12 (1972), 173.
|
[5] |
R. Bowen, Symbolic dynamics for hyperbolic flows,, Amer. J. Math., 95 (1973), 429.
|
[6] |
R. Bowen and B. Marcus, Unique ergodicity for horocycle foliations,, Israel J. Math., 26 (1977), 43.
|
[7] |
R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows,, Invent. Math., 29 (1975), 181.
|
[8] |
R. Bowen and P. Walters, Expansive one-parameter flows,, J. Differential Equations, 12 (1972), 180.
|
[9] |
M. Denker, C. Grillenberger and K. Sigmund, "Ergodic Theory on Compact Spaces,", Lecture Notes in Mathematics, (1976).
|
[10] |
S. J. Eigen and V. S. Prasad, Multiple Rokhlin tower theorem: A simple proof,, New York J. Math., (1997), 9.
|
[11] |
N. A. Friedman, "Introduction to Ergodic Theory,", Van Nostrand Reinhold Mathematical Studies, (1970).
|
[12] |
T. N. T. Goodman, Relating topological entropy and measure entropy,, Bull. London Math. Soc., 3 (1971), 176.
|
[13] |
R. I. Jewett, The prevalence of uniquely ergodic systems,, J. Math. Mech., 19 (): 717.
|
[14] |
M. Keane and M. Smorodinsky, A class of finitary codes,, Israel J. Math., 26 (1977), 352.
|
[15] |
M. Keane and M. Smorodinsky, Bernoulli schemes of the same entropy are finitarily isomorphic,, Ann. of Math. (2), 109 (1979), 397.
doi: 10.2307/1971117. |
[16] |
H. B. Keynes and J. B. Robertson, Eigenvalue theorems in topological transformation groups,, Trans. Amer. Math. Soc., 139 (1969), 359.
|
[17] |
W. Krieger, On entropy and generators of measure-preserving transformations,, Trans. Amer. Math. Soc., 149 (1970), 453.
|
[18] |
W. Krieger, On entropy and generators of measure-preserving transformations,, Trans. Amer. Math. Soc., 149 (1970), 453.
|
[19] |
W. Krieger, Erratum to: "On entropy and generators of measure-preserving transformations,", Trans. Amer. Math. Soc., 168 (1972).
|
[20] |
W. Krieger, On unique ergodicity,, in, (1972), 327.
|
[21] |
W. Krieger, On generators in ergodic theory,, in, (1975), 303.
|
[22] |
, F. Ledrappier, F. Rodriguez Hertz and J. Rodriguez Hertz,, personal communication., (). Google Scholar |
[23] |
D. Lind, Ergodic group automorphisms and specification,, in, 729 (1979), 93.
doi: 10.1007/BFb0063287. |
[24] |
D. Lind, Dynamical properties of quasihyperbolic toral automorphisms,, Ergodic Theory Dynam. Systems, 2 (1982), 49.
|
[25] |
D. Lind and B. Marcus, "An Introduction to Symbolic Dynamics and Coding,", Cambridge University Press, (1995).
doi: 10.1017/CBO9780511626302. |
[26] |
D. A. Lind, Perturbations of shifts of finite type,, SIAM J. Discrete Math., 2 (1989), 350.
doi: 10.1137/0402031. |
[27] |
D. A. Lind and J.-P. Thouvenot, Measure-preserving homeomorphisms of the torus represent all finite entropy ergodic transformations,, Math. Systems Theory, 11 (): 275.
|
[28] |
D. S. Ornstein, A $K$ automorphism with no square root and Pinsker's conjecture,, Advances in Math., 10 (1973), 89.
|
[29] |
W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics,, Astérisque, 187-188 (1990), 187.
|
[30] |
A. Quas and T. Soo, Ergodic universality of some topological dynamical systems,, \arXiv{1208.3501}, (2012). Google Scholar |
[31] |
M. Ratner, Markov partitions for Anosov flows on $n$-dimensional manifolds,, Israel J. Math., 15 (1973), 92.
|
[32] |
J. Serafin, Finitary codes, a short survey,, in, 48 (2006), 262.
doi: 10.1214/lnms/1196285827. |
[33] |
, J.-P. Thouvenot,, personal communication., (). Google Scholar |
[34] |
H. Totoki, On a class of special flows,, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 15 (1970), 157.
|
show all references
References:
[1] |
S. Alpern, Generic properties of measure preserving homeomorphisms,, In, 729 (1979), 16.
|
[2] |
A. Bellow and H. Furstenberg, An application of number theory to ergodic theory and the construction of uniquely ergodic models. A collection of invited papers on ergodic theory,, Israel J. Math., 33 (1979), 231.
doi: 10.1007/BF02762163. |
[3] |
R. Bowen, The equidistribution of closed geodesics,, Amer. J. Math., 94 (1972), 413.
|
[4] |
R. Bowen, One-dimensional hyperbolic sets for flows,, J. Differential Equations, 12 (1972), 173.
|
[5] |
R. Bowen, Symbolic dynamics for hyperbolic flows,, Amer. J. Math., 95 (1973), 429.
|
[6] |
R. Bowen and B. Marcus, Unique ergodicity for horocycle foliations,, Israel J. Math., 26 (1977), 43.
|
[7] |
R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows,, Invent. Math., 29 (1975), 181.
|
[8] |
R. Bowen and P. Walters, Expansive one-parameter flows,, J. Differential Equations, 12 (1972), 180.
|
[9] |
M. Denker, C. Grillenberger and K. Sigmund, "Ergodic Theory on Compact Spaces,", Lecture Notes in Mathematics, (1976).
|
[10] |
S. J. Eigen and V. S. Prasad, Multiple Rokhlin tower theorem: A simple proof,, New York J. Math., (1997), 9.
|
[11] |
N. A. Friedman, "Introduction to Ergodic Theory,", Van Nostrand Reinhold Mathematical Studies, (1970).
|
[12] |
T. N. T. Goodman, Relating topological entropy and measure entropy,, Bull. London Math. Soc., 3 (1971), 176.
|
[13] |
R. I. Jewett, The prevalence of uniquely ergodic systems,, J. Math. Mech., 19 (): 717.
|
[14] |
M. Keane and M. Smorodinsky, A class of finitary codes,, Israel J. Math., 26 (1977), 352.
|
[15] |
M. Keane and M. Smorodinsky, Bernoulli schemes of the same entropy are finitarily isomorphic,, Ann. of Math. (2), 109 (1979), 397.
doi: 10.2307/1971117. |
[16] |
H. B. Keynes and J. B. Robertson, Eigenvalue theorems in topological transformation groups,, Trans. Amer. Math. Soc., 139 (1969), 359.
|
[17] |
W. Krieger, On entropy and generators of measure-preserving transformations,, Trans. Amer. Math. Soc., 149 (1970), 453.
|
[18] |
W. Krieger, On entropy and generators of measure-preserving transformations,, Trans. Amer. Math. Soc., 149 (1970), 453.
|
[19] |
W. Krieger, Erratum to: "On entropy and generators of measure-preserving transformations,", Trans. Amer. Math. Soc., 168 (1972).
|
[20] |
W. Krieger, On unique ergodicity,, in, (1972), 327.
|
[21] |
W. Krieger, On generators in ergodic theory,, in, (1975), 303.
|
[22] |
, F. Ledrappier, F. Rodriguez Hertz and J. Rodriguez Hertz,, personal communication., (). Google Scholar |
[23] |
D. Lind, Ergodic group automorphisms and specification,, in, 729 (1979), 93.
doi: 10.1007/BFb0063287. |
[24] |
D. Lind, Dynamical properties of quasihyperbolic toral automorphisms,, Ergodic Theory Dynam. Systems, 2 (1982), 49.
|
[25] |
D. Lind and B. Marcus, "An Introduction to Symbolic Dynamics and Coding,", Cambridge University Press, (1995).
doi: 10.1017/CBO9780511626302. |
[26] |
D. A. Lind, Perturbations of shifts of finite type,, SIAM J. Discrete Math., 2 (1989), 350.
doi: 10.1137/0402031. |
[27] |
D. A. Lind and J.-P. Thouvenot, Measure-preserving homeomorphisms of the torus represent all finite entropy ergodic transformations,, Math. Systems Theory, 11 (): 275.
|
[28] |
D. S. Ornstein, A $K$ automorphism with no square root and Pinsker's conjecture,, Advances in Math., 10 (1973), 89.
|
[29] |
W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics,, Astérisque, 187-188 (1990), 187.
|
[30] |
A. Quas and T. Soo, Ergodic universality of some topological dynamical systems,, \arXiv{1208.3501}, (2012). Google Scholar |
[31] |
M. Ratner, Markov partitions for Anosov flows on $n$-dimensional manifolds,, Israel J. Math., 15 (1973), 92.
|
[32] |
J. Serafin, Finitary codes, a short survey,, in, 48 (2006), 262.
doi: 10.1214/lnms/1196285827. |
[33] |
, J.-P. Thouvenot,, personal communication., (). Google Scholar |
[34] |
H. Totoki, On a class of special flows,, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 15 (1970), 157.
|
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