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Simple skew category algebras associated with minimal partially defined dynamical systems
Endomorphisms of Sturmian systems and the discrete chair substitution tiling system
1. | Dominican University, 7900 W. Division Street, River Forest, IL 60305, United States |
References:
[1] |
Ethan M. Coven, Endomorphisms of substitution minimal sets, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 20 (1971/72), 129-133. |
[2] |
Tomasz Downarowicz, The royal couple conceals their mutual relationship: A noncoalescent Toeplitz flow, Israel J. Math., 97 (1997), 239-251.
doi: 10.1007/BF02774039. |
[3] |
Tomasz Downarowicz, Survey of odometers and Toeplitz flows, in "Algebraic and Topological Dynamics," Contemp. Math., 385, Amer. Math. Soc., Providence, RI, (2005), 7-37.
doi: 10.1090/conm/385/07188. |
[4] |
N. Pytheas Fogg, "Substitutions in Dynamics, Arithmetics and Combinatorics," eds. V. Berthé, S. Ferenczi, C. Mauduit and A. Siegel, Lecture Notes in Mathematics, 1794, Springer-Verlang, Berlin, 2002.
doi: 10.1007/b13861. |
[5] |
Natalie Priebe Frank, A primer of substitution tilings of the Euclidean plane, Expo. Math., 26 (2008), 295-326.
doi: 10.1016/j.exmath.2008.02.001. |
[6] |
Harry Furstenberg, Harvey Keynes and Leonard Shapiro, Prime flows in topological dynamics, Israel J. Math., 14 (1973), 26-38. |
[7] |
Paul R. Halmos and J. von Neumann, Operator methods in classical mechanics. II, Ann. of Math. (2), 43 (1942), 332-350. |
[8] |
G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory, 3 (1969), 320-375. |
[9] |
Charles Holton, Charles Radin and Lorenzo Sadun, Conjugacies for tiling dynamical systems, Comm. Math. Phys., 254 (2005), 343-359. |
[10] |
Douglas Lind and Brian Marcus, "An Introduction to Symbolic Dynamics and Coding," Cambridge University Press, Cambridge, 1995. |
[11] |
Marston Morse and Gustav A. Hedlund, Symbolic dynamics. II. Sturmian trajectories, Amer. J. Math., 62 (1940), 1-42. |
[12] |
James R. Munkres, "Topology: A First Course," Prentice-Hall Inc., Englewood Cliffs, N.J., 1975. |
[13] |
Jeanette Olli, "Dynamical Systems, Division Point Measures, and Endomorphisms," Ph.D thesis, University of North Carolina at Chapel Hill, 2009. |
[14] |
Michael E. Paul, Construction of almost automorphic symbolic minimal flows, General Topology and Appl., 6 (1976), 45-56. |
[15] |
Karl Petersen, On a series of cosecants related to a problem in ergodic theory, Compositio Math., 26 (1973), 313-317. |
[16] |
Karl Petersen and Leonard Shapiro, Induced flows, Trans. Amer. Math. Soc., 177 (1973), 375-390. |
[17] |
Charles Radin, Space tilings and substitutions, Geom. Dedicata, 55 (1995), 257-264. |
[18] |
Charles Radin, Symmetry of tilings of the plane, Bull. Amer. Math. Soc. (N.S.), 29 (1993), 213-217. |
[19] |
E. Arthur Robinson, Jr., On the table and the chair, Indag. Math. (N.S.), 10 (1999), 581-599. |
[20] |
E. Arthur Robinson, Jr., Symbolic dynamics and tilings of $\mathbbmathbb{R}^{d}$, in "Symbolic Dynamics and its Applications," Amer. Math. Soc., (2004), 81-119. |
[21] |
L. Sadun, Tilings, tiling spaces and topology, Philosophical Magazine, 86 (2006), 875-881. |
[22] |
William A. Veech, Point-distal flows, Amer. J. Math., 92 (1970), 205-242. |
show all references
References:
[1] |
Ethan M. Coven, Endomorphisms of substitution minimal sets, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 20 (1971/72), 129-133. |
[2] |
Tomasz Downarowicz, The royal couple conceals their mutual relationship: A noncoalescent Toeplitz flow, Israel J. Math., 97 (1997), 239-251.
doi: 10.1007/BF02774039. |
[3] |
Tomasz Downarowicz, Survey of odometers and Toeplitz flows, in "Algebraic and Topological Dynamics," Contemp. Math., 385, Amer. Math. Soc., Providence, RI, (2005), 7-37.
doi: 10.1090/conm/385/07188. |
[4] |
N. Pytheas Fogg, "Substitutions in Dynamics, Arithmetics and Combinatorics," eds. V. Berthé, S. Ferenczi, C. Mauduit and A. Siegel, Lecture Notes in Mathematics, 1794, Springer-Verlang, Berlin, 2002.
doi: 10.1007/b13861. |
[5] |
Natalie Priebe Frank, A primer of substitution tilings of the Euclidean plane, Expo. Math., 26 (2008), 295-326.
doi: 10.1016/j.exmath.2008.02.001. |
[6] |
Harry Furstenberg, Harvey Keynes and Leonard Shapiro, Prime flows in topological dynamics, Israel J. Math., 14 (1973), 26-38. |
[7] |
Paul R. Halmos and J. von Neumann, Operator methods in classical mechanics. II, Ann. of Math. (2), 43 (1942), 332-350. |
[8] |
G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory, 3 (1969), 320-375. |
[9] |
Charles Holton, Charles Radin and Lorenzo Sadun, Conjugacies for tiling dynamical systems, Comm. Math. Phys., 254 (2005), 343-359. |
[10] |
Douglas Lind and Brian Marcus, "An Introduction to Symbolic Dynamics and Coding," Cambridge University Press, Cambridge, 1995. |
[11] |
Marston Morse and Gustav A. Hedlund, Symbolic dynamics. II. Sturmian trajectories, Amer. J. Math., 62 (1940), 1-42. |
[12] |
James R. Munkres, "Topology: A First Course," Prentice-Hall Inc., Englewood Cliffs, N.J., 1975. |
[13] |
Jeanette Olli, "Dynamical Systems, Division Point Measures, and Endomorphisms," Ph.D thesis, University of North Carolina at Chapel Hill, 2009. |
[14] |
Michael E. Paul, Construction of almost automorphic symbolic minimal flows, General Topology and Appl., 6 (1976), 45-56. |
[15] |
Karl Petersen, On a series of cosecants related to a problem in ergodic theory, Compositio Math., 26 (1973), 313-317. |
[16] |
Karl Petersen and Leonard Shapiro, Induced flows, Trans. Amer. Math. Soc., 177 (1973), 375-390. |
[17] |
Charles Radin, Space tilings and substitutions, Geom. Dedicata, 55 (1995), 257-264. |
[18] |
Charles Radin, Symmetry of tilings of the plane, Bull. Amer. Math. Soc. (N.S.), 29 (1993), 213-217. |
[19] |
E. Arthur Robinson, Jr., On the table and the chair, Indag. Math. (N.S.), 10 (1999), 581-599. |
[20] |
E. Arthur Robinson, Jr., Symbolic dynamics and tilings of $\mathbbmathbb{R}^{d}$, in "Symbolic Dynamics and its Applications," Amer. Math. Soc., (2004), 81-119. |
[21] |
L. Sadun, Tilings, tiling spaces and topology, Philosophical Magazine, 86 (2006), 875-881. |
[22] |
William A. Veech, Point-distal flows, Amer. J. Math., 92 (1970), 205-242. |
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