- Previous Article
- DCDS-B Home
- This Issue
-
Next Article
Topological mixing, knot points and bounds of topological entropy
Projective distance and $g$-measures
1. | Instituto de Física, Universidad Autónoma de San Luis Potosí, Avenida Manuel Nava 6, Zona Universitaria, 78290 San Luis Potosí, Mexico, Mexico |
References:
[1] |
G. Birkhoff, Extensions of Jentzch's theorem, Transactions of the American Mathematical Society, 85 (1957), 219-227. |
[2] |
M. Bramson and S. Kalikow, Nonuniqueness in $g$-Functions, Israel Journal of Mathematics, 84 (1993), 153-160.
doi: 10.1007/BF02761697. |
[3] |
X. Bressaud, R. Fernández and A. Galves, Speed of $\bard$-convergence for Markov approximations of chains with complete connections. A coupling approach, Stochastic Processes and Applications, 83 (1999), 127-138.
doi: 10.1016/S0304-4149(99)00025-3. |
[4] |
J.-R. Chazottes, E. Floriani and R. Lima, Relative entropy and identification of Gibbs measures in dynamical systems, Journal of Statistical Physics, 90 (1998), 697-725.
doi: 10.1023/A:1023220802597. |
[5] |
J.-R. Chazottes, L. Ramirez and E. Ugalde, Finite type approximations of Gibbs measures on sofic subshifts, Nonlinearity, 18 (2005), 445-463.
doi: 10.1088/0951-7715/18/1/023. |
[6] |
J.-R. Chazottes and E. Ugalde, On the preservation of Gibbsianness under symbol amalgamation, in Entropy of Hidden Markov Processes and Connections to Dynamical Systems, Cambridge University Press, 2011, 72-97. |
[7] |
Z. Coelho and A. Quas, Criteria for $\bard$-continuity, Transactions of the American Mathematical Society, 350 (1998), 3257-3268.
doi: 10.1090/S0002-9947-98-01923-0. |
[8] |
M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Mathematics, 527, Springer-Verlag, 1976. |
[9] |
F. Dyson, Existence of a phase-transition in a one-dimesional Ising ferromagnet, Communications in Mathematical Physics, 12 (1969), 91-107.
doi: 10.1007/BF01645907. |
[10] |
P. Ferrero and B. Schmitt, Théorème de Ruelle-Perron-Frobenius et Métriques Projectives,, 1979., ().
|
[11] |
J. Fröhlich and T. Spencer, The phase transition in the one-dimensional Ising model with $1/r^2$ interaction energy, Communications in Mathematical Physics, 84 (1982), 87-101.
doi: 10.1007/BF01208373. |
[12] |
D. Hilbert, Ueber die Gerade Linie als körzeste Verbindung zweier Punkte, Mathematische Annalen, 46 (1885), 91-96. |
[13] |
P. Hulse, An example of non-unique $g$-measures, Ergodic Theory and Dynamical Systems, 26 (2006), 439-445.
doi: 10.1017/S0143385705000489. |
[14] |
M. Keane, Strongly Mixing $g$-Measures, Inventiones Mathematicae, 16 (1972), 309-324.
doi: 10.1007/BF01425715. |
[15] |
G. Keller, Equilibrium States in Ergodic Theory, London Mathematical Society, Student Texts, 42, 1998. |
[16] |
F. Ledrappier, Principe variationnel et systèmes dynamiques symboliques, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiet, 30 (1974), 185-202.
doi: 10.1007/BF00533471. |
[17] |
C. Liverani, Decay of correlations, Annals of Mathematics, 142 (1995), 239-301.
doi: 10.2307/2118636. |
[18] |
C. Liverani, Decay of correlations for piecewise expanding maps, Journal of Statistical Physics, 78 (1995), 1111-1129.
doi: 10.1007/BF02183704. |
[19] |
C. Liverani, B. Saussol and S. Vaienti, Conformal measure and decay of correlation for covering weighted systems, Ergodic Theory and Dynamical Systems, 18 (1998), 1399-1420.
doi: 10.1017/S0143385798118023. |
[20] |
C. Maldonado and R. Salgado-García, Markov approximations of Gibbs measures for long-range interactions on 1D lattices, Journal of Statistical Mechanics: Theory and Experiment, 2013 (2013), P08012. |
[21] |
K. Marton, Bounding $\bard$-distance by informational divergence: A method to prove measure concentration, Annals of Probability, 24 (1996), 857-866.
doi: 10.1214/aop/1039639365. |
[22] |
K. Marton, Measure concentration for a class of random processes, Probability Theory and Related Fields, 110 (1998), 427-439.
doi: 10.1007/s004400050154. |
[23] |
V. Maume-Deschamps, Correlation decay for Markov maps on a countable state space, Ergodic Theory and Dynamical Systems, 21 (2001), 165-196.
doi: 10.1017/S0143385701001110. |
[24] |
V. Maume-Deschamps, Projective metric and mixing properties on towers, Transactions of the American Mathematical Society, 353 (2001), 3371-3389.
doi: 10.1090/S0002-9947-01-02786-6. |
[25] |
O. Onicescu and G. Mihoc, Sur les Chaînes de variables statistiques, Bulletin de Sciences Mathématiques, 59 (1935), 174-192. |
[26] |
D. S. Ornstein, An application of ergodic theory to probability theory, The Annals of Probability, 1 (1973), 43-65.
doi: 10.1214/aop/1176997024. |
[27] |
R. Salgado-García and E. Ugalde, Exact scaling in the expansion-modification system, Journal of Statistical Physics, 153 (2013), 842-863.
doi: 10.1007/s10955-013-0866-x. |
[28] |
E. Seneta, Non-negative matrices an Markov Chains, $2^{nd}$ edition, Springer-Verlag, 1973. |
[29] |
P. Shields, Ergodic Theory of Discrete Sample Paths, Graduate Studies in Mathematics, 13, American Mathematical Society, 1996. |
[30] |
P. Walters, Ruelle's operator theorem and $g$-measures, Transactions of the American Mathematical Society, 214 (1975), 375-387. |
show all references
References:
[1] |
G. Birkhoff, Extensions of Jentzch's theorem, Transactions of the American Mathematical Society, 85 (1957), 219-227. |
[2] |
M. Bramson and S. Kalikow, Nonuniqueness in $g$-Functions, Israel Journal of Mathematics, 84 (1993), 153-160.
doi: 10.1007/BF02761697. |
[3] |
X. Bressaud, R. Fernández and A. Galves, Speed of $\bard$-convergence for Markov approximations of chains with complete connections. A coupling approach, Stochastic Processes and Applications, 83 (1999), 127-138.
doi: 10.1016/S0304-4149(99)00025-3. |
[4] |
J.-R. Chazottes, E. Floriani and R. Lima, Relative entropy and identification of Gibbs measures in dynamical systems, Journal of Statistical Physics, 90 (1998), 697-725.
doi: 10.1023/A:1023220802597. |
[5] |
J.-R. Chazottes, L. Ramirez and E. Ugalde, Finite type approximations of Gibbs measures on sofic subshifts, Nonlinearity, 18 (2005), 445-463.
doi: 10.1088/0951-7715/18/1/023. |
[6] |
J.-R. Chazottes and E. Ugalde, On the preservation of Gibbsianness under symbol amalgamation, in Entropy of Hidden Markov Processes and Connections to Dynamical Systems, Cambridge University Press, 2011, 72-97. |
[7] |
Z. Coelho and A. Quas, Criteria for $\bard$-continuity, Transactions of the American Mathematical Society, 350 (1998), 3257-3268.
doi: 10.1090/S0002-9947-98-01923-0. |
[8] |
M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Mathematics, 527, Springer-Verlag, 1976. |
[9] |
F. Dyson, Existence of a phase-transition in a one-dimesional Ising ferromagnet, Communications in Mathematical Physics, 12 (1969), 91-107.
doi: 10.1007/BF01645907. |
[10] |
P. Ferrero and B. Schmitt, Théorème de Ruelle-Perron-Frobenius et Métriques Projectives,, 1979., ().
|
[11] |
J. Fröhlich and T. Spencer, The phase transition in the one-dimensional Ising model with $1/r^2$ interaction energy, Communications in Mathematical Physics, 84 (1982), 87-101.
doi: 10.1007/BF01208373. |
[12] |
D. Hilbert, Ueber die Gerade Linie als körzeste Verbindung zweier Punkte, Mathematische Annalen, 46 (1885), 91-96. |
[13] |
P. Hulse, An example of non-unique $g$-measures, Ergodic Theory and Dynamical Systems, 26 (2006), 439-445.
doi: 10.1017/S0143385705000489. |
[14] |
M. Keane, Strongly Mixing $g$-Measures, Inventiones Mathematicae, 16 (1972), 309-324.
doi: 10.1007/BF01425715. |
[15] |
G. Keller, Equilibrium States in Ergodic Theory, London Mathematical Society, Student Texts, 42, 1998. |
[16] |
F. Ledrappier, Principe variationnel et systèmes dynamiques symboliques, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiet, 30 (1974), 185-202.
doi: 10.1007/BF00533471. |
[17] |
C. Liverani, Decay of correlations, Annals of Mathematics, 142 (1995), 239-301.
doi: 10.2307/2118636. |
[18] |
C. Liverani, Decay of correlations for piecewise expanding maps, Journal of Statistical Physics, 78 (1995), 1111-1129.
doi: 10.1007/BF02183704. |
[19] |
C. Liverani, B. Saussol and S. Vaienti, Conformal measure and decay of correlation for covering weighted systems, Ergodic Theory and Dynamical Systems, 18 (1998), 1399-1420.
doi: 10.1017/S0143385798118023. |
[20] |
C. Maldonado and R. Salgado-García, Markov approximations of Gibbs measures for long-range interactions on 1D lattices, Journal of Statistical Mechanics: Theory and Experiment, 2013 (2013), P08012. |
[21] |
K. Marton, Bounding $\bard$-distance by informational divergence: A method to prove measure concentration, Annals of Probability, 24 (1996), 857-866.
doi: 10.1214/aop/1039639365. |
[22] |
K. Marton, Measure concentration for a class of random processes, Probability Theory and Related Fields, 110 (1998), 427-439.
doi: 10.1007/s004400050154. |
[23] |
V. Maume-Deschamps, Correlation decay for Markov maps on a countable state space, Ergodic Theory and Dynamical Systems, 21 (2001), 165-196.
doi: 10.1017/S0143385701001110. |
[24] |
V. Maume-Deschamps, Projective metric and mixing properties on towers, Transactions of the American Mathematical Society, 353 (2001), 3371-3389.
doi: 10.1090/S0002-9947-01-02786-6. |
[25] |
O. Onicescu and G. Mihoc, Sur les Chaînes de variables statistiques, Bulletin de Sciences Mathématiques, 59 (1935), 174-192. |
[26] |
D. S. Ornstein, An application of ergodic theory to probability theory, The Annals of Probability, 1 (1973), 43-65.
doi: 10.1214/aop/1176997024. |
[27] |
R. Salgado-García and E. Ugalde, Exact scaling in the expansion-modification system, Journal of Statistical Physics, 153 (2013), 842-863.
doi: 10.1007/s10955-013-0866-x. |
[28] |
E. Seneta, Non-negative matrices an Markov Chains, $2^{nd}$ edition, Springer-Verlag, 1973. |
[29] |
P. Shields, Ergodic Theory of Discrete Sample Paths, Graduate Studies in Mathematics, 13, American Mathematical Society, 1996. |
[30] |
P. Walters, Ruelle's operator theorem and $g$-measures, Transactions of the American Mathematical Society, 214 (1975), 375-387. |
[1] |
Raz Kupferman, Asaf Shachar. On strain measures and the geodesic distance to $SO_n$ in the general linear group. Journal of Geometric Mechanics, 2016, 8 (4) : 437-460. doi: 10.3934/jgm.2016015 |
[2] |
Xiongping Dai, Yunping Jiang. Distance entropy of dynamical systems on noncompact-phase spaces. Discrete and Continuous Dynamical Systems, 2008, 20 (2) : 313-333. doi: 10.3934/dcds.2008.20.313 |
[3] |
José M. Arrieta, Esperanza Santamaría. Estimates on the distance of inertial manifolds. Discrete and Continuous Dynamical Systems, 2014, 34 (10) : 3921-3944. doi: 10.3934/dcds.2014.34.3921 |
[4] |
Mario Bukal. Well-posedness and convergence of a numerical scheme for the corrected Derrida-Lebowitz-Speer-Spohn equation using the Hellinger distance. Discrete and Continuous Dynamical Systems, 2021, 41 (7) : 3389-3414. doi: 10.3934/dcds.2021001 |
[5] |
Konstantinos Drakakis, Roderick Gow, Scott Rickard. Common distance vectors between Costas arrays. Advances in Mathematics of Communications, 2009, 3 (1) : 35-52. doi: 10.3934/amc.2009.3.35 |
[6] |
Chun-Xiang Guo, Guo Qiang, Jin Mao-Zhu, Zhihan Lv. Dynamic systems based on preference graph and distance. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1139-1154. doi: 10.3934/dcdss.2015.8.1139 |
[7] |
Yujuan Li, Guizhen Zhu. On the error distance of extended Reed-Solomon codes. Advances in Mathematics of Communications, 2016, 10 (2) : 413-427. doi: 10.3934/amc.2016015 |
[8] |
John Sheekey. A new family of linear maximum rank distance codes. Advances in Mathematics of Communications, 2016, 10 (3) : 475-488. doi: 10.3934/amc.2016019 |
[9] |
Sobhan Seyfaddini. Unboundedness of the Lagrangian Hofer distance in the Euclidean ball. Electronic Research Announcements, 2014, 21: 1-7. doi: 10.3934/era.2014.21.1 |
[10] |
Atsushi Katsuda, Yaroslav Kurylev, Matti Lassas. Stability of boundary distance representation and reconstruction of Riemannian manifolds. Inverse Problems and Imaging, 2007, 1 (1) : 135-157. doi: 10.3934/ipi.2007.1.135 |
[11] |
Carlos Munuera, Morgan Barbier. Wet paper codes and the dual distance in steganography. Advances in Mathematics of Communications, 2012, 6 (3) : 273-285. doi: 10.3934/amc.2012.6.273 |
[12] |
San Ling, Buket Özkaya. New bounds on the minimum distance of cyclic codes. Advances in Mathematics of Communications, 2021, 15 (1) : 1-8. doi: 10.3934/amc.2020038 |
[13] |
Xin Yang Lu. Regularity of densities in relaxed and penalized average distance problem. Networks and Heterogeneous Media, 2015, 10 (4) : 837-855. doi: 10.3934/nhm.2015.10.837 |
[14] |
Jinmei Fan, Yanhai Zhang. Optimal quinary negacyclic codes with minimum distance four. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021043 |
[15] |
Michel C. Delfour. Hadamard Semidifferential, Oriented Distance Function, and some Applications. Communications on Pure and Applied Analysis, 2022, 21 (6) : 1917-1951. doi: 10.3934/cpaa.2021076 |
[16] |
Wael Bahsoun, Paweł Góra. SRB measures for certain Markov processes. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 17-37. doi: 10.3934/dcds.2011.30.17 |
[17] |
Carlos Munuera, Fernando Torres. A note on the order bound on the minimum distance of AG codes and acute semigroups. Advances in Mathematics of Communications, 2008, 2 (2) : 175-181. doi: 10.3934/amc.2008.2.175 |
[18] |
Liping Tang, Ying Gao. Some properties of nonconvex oriented distance function and applications to vector optimization problems. Journal of Industrial and Management Optimization, 2021, 17 (1) : 485-500. doi: 10.3934/jimo.2020117 |
[19] |
Sohana Jahan. Supervised distance preserving projection using alternating direction method of multipliers. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1783-1799. doi: 10.3934/jimo.2019029 |
[20] |
Andries E. Brouwer, Tuvi Etzion. Some new distance-4 constant weight codes. Advances in Mathematics of Communications, 2011, 5 (3) : 417-424. doi: 10.3934/amc.2011.5.417 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]