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A class of mixing special flows over two--dimensional rotations
Ergodicity of two particles with attractive interaction
| 1. | Institut für Statistik und Wahrscheinlichkeitstheorie, TU Wien, 1040 Wien, Austria |
| 2. | Institut für Theoretische Physik, TU Wien, 1040 Wien, Austria |
References:
| [1] |
V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer, 1989.
doi: 10.1007/978-1-4757-2063-1. |
| [2] |
R. J. Baxter, Exactly solved models in statistical mechanics, Academic Press, 1982. |
| [3] |
L. Boltzmann, Vorlesungen Über Gastheorie, Barth, 1896. |
| [4] |
M. Boshernitzan, A condition for minimal interval exchange maps to be uniquely ergodic, Duke Mathematical Journal, 52 (1985), 723-752.
doi: 10.1215/S0012-7094-85-05238-X. |
| [5] |
G. R. Brannock and J. K. Percus, Wertheim cluster development of free energy functionals for general nearest-neighbor interactions in $D=1$, The Journal of Chemical Physics, 105 (1996), 614-627.
doi: 10.1063/1.471920. |
| [6] |
J. A. Cuesta and C. Tutschka, Overcomplete free energy functional for $D=1$ particle systems with next neighbor interactions, Journal of Statistical Physics, 111 (2003), 1125-1148.
doi: 10.1023/A:1023096031180. |
| [7] |
K. F. Herzfeld and M. Goeppert-Mayer, On the states of aggregation, The Journal of Chemical Physics, 2 (1934), 38-45.
doi: 10.1063/1.1749355. |
| [8] |
M. Keane, Interval exchange transformations, Mathematische Zeitschrift, 141 (1975), 25-31.
doi: 10.1007/BF01236981. |
| [9] |
S. Kerckhoff, H. Masur and J. Smillie, Ergodicity of billiard flows and quadratic differentials, Annals of Mathematics, 124 (1986), 293-311.
doi: 10.2307/1971280. |
| [10] |
A. I. Khinchin, Mathematical Foundations of Statistical Mechanics, Dover, 1949. |
| [11] |
H. Masur, Interval exchange transformations and measured foliations, Annals of Mathematics, 115 (1982), 169-200.
doi: 10.2307/1971341. |
| [12] |
A. van der Poorten, Fermat's four squares theorem, 2007. Available from: http://maths.mq.edu.au/~alf/SomeRecentPapers/183.pdf. |
| [13] |
D. Ruelle, Statistical Mechanics: Rigorous Results, Benjamin, 1969. |
| [14] |
W. A. Veech, Gauss measures for transformations on the space of interval exchange maps, Annals of Mathematics, 115 (1982), 201-242.
doi: 10.2307/1971391. |
show all references
References:
| [1] |
V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer, 1989.
doi: 10.1007/978-1-4757-2063-1. |
| [2] |
R. J. Baxter, Exactly solved models in statistical mechanics, Academic Press, 1982. |
| [3] |
L. Boltzmann, Vorlesungen Über Gastheorie, Barth, 1896. |
| [4] |
M. Boshernitzan, A condition for minimal interval exchange maps to be uniquely ergodic, Duke Mathematical Journal, 52 (1985), 723-752.
doi: 10.1215/S0012-7094-85-05238-X. |
| [5] |
G. R. Brannock and J. K. Percus, Wertheim cluster development of free energy functionals for general nearest-neighbor interactions in $D=1$, The Journal of Chemical Physics, 105 (1996), 614-627.
doi: 10.1063/1.471920. |
| [6] |
J. A. Cuesta and C. Tutschka, Overcomplete free energy functional for $D=1$ particle systems with next neighbor interactions, Journal of Statistical Physics, 111 (2003), 1125-1148.
doi: 10.1023/A:1023096031180. |
| [7] |
K. F. Herzfeld and M. Goeppert-Mayer, On the states of aggregation, The Journal of Chemical Physics, 2 (1934), 38-45.
doi: 10.1063/1.1749355. |
| [8] |
M. Keane, Interval exchange transformations, Mathematische Zeitschrift, 141 (1975), 25-31.
doi: 10.1007/BF01236981. |
| [9] |
S. Kerckhoff, H. Masur and J. Smillie, Ergodicity of billiard flows and quadratic differentials, Annals of Mathematics, 124 (1986), 293-311.
doi: 10.2307/1971280. |
| [10] |
A. I. Khinchin, Mathematical Foundations of Statistical Mechanics, Dover, 1949. |
| [11] |
H. Masur, Interval exchange transformations and measured foliations, Annals of Mathematics, 115 (1982), 169-200.
doi: 10.2307/1971341. |
| [12] |
A. van der Poorten, Fermat's four squares theorem, 2007. Available from: http://maths.mq.edu.au/~alf/SomeRecentPapers/183.pdf. |
| [13] |
D. Ruelle, Statistical Mechanics: Rigorous Results, Benjamin, 1969. |
| [14] |
W. A. Veech, Gauss measures for transformations on the space of interval exchange maps, Annals of Mathematics, 115 (1982), 201-242.
doi: 10.2307/1971391. |
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