Equilibrium states of grid functions
Authors:
Nelson G. Markley and Michael E. Paul
Journal:
Trans. Amer. Math. Soc. 274 (1982), 169191
MSC:
Primary 28D20; Secondary 54H20
MathSciNet review:
670926
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Abstract: It is well known that locally constant functions on symbolic spaces have unique equilibrium states. In this paper we investigate the nature of equilibrium states for a type of continuous function which need not have a finite range. Although most of these functions have a unique equilibrium state, phase transitions or multiple equilibrium states do occur and can be analyzed.
 [1]
M. Fisher, The theory of condensation and the critical point, Physics 3 (1967), 255283.
 [2]
Franz
Hofbauer, Examples for the nonuniqueness of the
equilibrium state, Trans. Amer. Math. Soc.
228 (1977), no. 223–241.. MR 0435352
(55 #8312), http://dx.doi.org/10.1090/S00029947197704353521
 [3]
M.
Kac, On the notion of recurrence in
discrete stochastic processes, Bull. Amer.
Math. Soc. 53
(1947), 1002–1010. MR 0022323
(9,194a), http://dx.doi.org/10.1090/S000299041947089278
 [4]
N. Markley and M. Paul, Equilibrium states supported on periodic orbits, University of Maryland Technical Report TR 7850.
 [5]
, Equilibrium states of grid functions, University of Maryland Technical Report TR 8073.
 [6]
David
Ruelle, Thermodynamic formalism, Encyclopedia of Mathematics
and its Applications, vol. 5, AddisonWesley Publishing Co., Reading,
Mass., 1978. The mathematical structures of classical equilibrium
statistical mechanics; With a foreword by Giovanni Gallavotti and
GianCarlo Rota. MR 511655
(80g:82017)
 [7]
Richard
S. Varga, Matrix iterative analysis, PrenticeHall Inc.,
Englewood Cliffs, N.J., 1962. MR 0158502
(28 #1725)
 [8]
Peter
Walters, Ruelle’s operator theorem and
𝑔measures, Trans. Amer. Math. Soc.
214 (1975),
375–387. MR 0412389
(54 #515), http://dx.doi.org/10.1090/S00029947197504123898
 [9]
Peter
Walters, A variational principle for the pressure of continuous
transformations, Amer. J. Math. 97 (1975),
no. 4, 937–971. MR 0390180
(52 #11006)
 [10]
Peter
Walters, Invariant measures and equilibrium
states for some mappings which expand distances, Trans. Amer. Math. Soc. 236 (1978), 121–153. MR 0466493
(57 #6371), http://dx.doi.org/10.1090/S00029947197804664931
 [1]
 M. Fisher, The theory of condensation and the critical point, Physics 3 (1967), 255283.
 [2]
 F. Hofbauer, Examples for the nonuniqueness of the equilibrium state, Trans. Amer. Math. Soc. 228 (1977), 223241. MR 0435352 (55:8312)
 [3]
 M. Kac, On the notion of recurrence in discrete stochastic processes, Bull. Amer. Math. Soc. 53 (1947), 10021010. MR 0022323 (9:194a)
 [4]
 N. Markley and M. Paul, Equilibrium states supported on periodic orbits, University of Maryland Technical Report TR 7850.
 [5]
 , Equilibrium states of grid functions, University of Maryland Technical Report TR 8073.
 [6]
 D. Ruelle, Thermodynamic formalism, AddisonWesley, Reading, Mass., 1978. MR 511655 (80g:82017)
 [7]
 R. Varga, Matrix iterative analysis, PrenticeHall, Englewood Cliffs, N.J., 1962. MR 0158502 (28:1725)
 [8]
 P. Walters, Ruelle's operator theorem and measures, Trans. Amer. Math. Soc. 214 (1975), 375387. MR 0412389 (54:515)
 [9]
 , A variational principle for the pressure of continuous transformations, Amer. J. Math. 97 (1976), 937971. MR 0390180 (52:11006)
 [10]
 , Invariant measures and equilibrium states for some mappings which expand distances, Trans. Amer. Math. Soc. 236 (1978), 121153. MR 0466493 (57:6371)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198206709266
PII:
S 00029947(1982)06709266
Article copyright:
© Copyright 1982 American Mathematical Society
