A zero-dimensional (resp. symbolic) flow is a suspension flow over a zero-dimensional system (resp. a subshift). We show that any topological flow admits a principal extension by a zero-dimensional flow. Following [
Citation: |
[1] |
L. M. Abramov, On the entropy of a flow, Dokl. Akad. Nauk SSSR, 128 (1959), 873-875.
![]() ![]() |
[2] |
M. Beboutoff and W. Stepanoff, Sur la mesure invariante dans les systemes dynamiques qui ne different que par le temps, Rec. Math. [Mat. Sbornik] N.S., 7 (1940), 143-166.
![]() ![]() |
[3] |
R. Bowen and P. Walters, Expansive one-parameter flows, J. Differential Equations, 12 (1972), 180-193.
doi: 10.1016/0022-0396(72)90013-7.![]() ![]() ![]() |
[4] |
M. Boyle and T. Downarowicz, The entropy theory of symbolic extensions, Invent. Math., 156 (2004), 119-161.
doi: 10.1007/s00222-003-0335-2.![]() ![]() ![]() |
[5] |
M. Boyle, D. Fiebig and U. Fiebig, Residual entropy, conditional entropy and subshift covers, Forum Math., 14 (2002), 713-757.
doi: 10.1515/form.2002.031.![]() ![]() ![]() |
[6] |
D. Burguet, Symbolic extensions and uniform generators for topological regular flows, J. Differential Equations, 267 (2019), 4320-4372.
doi: 10.1016/j.jde.2019.05.001.![]() ![]() ![]() |
[7] |
D. Burguet and T. Downarowicz, Uniform generators, symbolic extensions with an embedding, and structure of periodic orbits, J. Dynam. Differential Equations, 31 (2019), 815-852.
doi: 10.1007/s10884-018-9674-y.![]() ![]() ![]() |
[8] |
T. Downarowicz, Entropy structure, J. Anal. Math., 96 (2005), 57-116.
doi: 10.1007/BF02787825.![]() ![]() ![]() |
[9] |
T. Downarowicz, Entropy in Dynamical Systems, New Mathematical Monographs, 18. Cambridge University Press, Cambridge, 2011.
doi: 10.1017/CBO9780511976155.![]() ![]() ![]() |
[10] |
T. Downarowicz and D. Huczek, Zero-dimensional principal extensions, Acta Appl. Math., 126 (2013), 117-129.
doi: 10.1007/s10440-013-9810-y.![]() ![]() ![]() |
[11] |
F. Ledrappier and P. Walters, A relativised variational principle for continuous transformations, J. London Math. Soc., 16 (1977), 568-576.
doi: 10.1112/jlms/s2-16.3.568.![]() ![]() ![]() |
[12] |
E. Lindenstrauss, Mean dimension, small entropy factors and an embedding theorem, Inst. Hautes Études Sci. Publ. Math., (1999), 227–262.
![]() ![]() |
[13] |
T. Ohno, A weak equivalence and topological entropy, Publ. Res. Inst. Math. Sci., 16 (1980), 289-298.
doi: 10.2977/prims/1195187508.![]() ![]() ![]() |
[14] |
W. Sun and C. Zhang, Zero entropy versus infinite entropy, Discrete Contin. Dyn. Syst., 30 (2011), 1237-1242.
doi: 10.3934/dcds.2011.30.1237.![]() ![]() ![]() |