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Chaotic Delone sets
On fair entropy of the tent family
1. | School of Mathematics, Hunan University, Changsha 410082, China |
2. | College of Mathematics, Sichuan University, Chengdu 610064, China |
The notions of fair measure and fair entropy were introduced by Misiurewicz and Rodrigues [
References:
[1] |
V. Baladi, Positive Transfer Operators and Decay of Correlations, volume 16 of Advanced Series in Nonlinear Dynamics, World Scientific Publishing Co., Inc., River Edge, NJ, 2000.
doi: 10.1142/9789812813633. |
[2] |
V. Baladi and D. Ruelle,
An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps, Ergodic Theory Dynam. Systems, 14 (1994), 621-632.
doi: 10.1017/S0143385700008087. |
[3] |
O. F. Bandtlow and H. H. Rugh,
Entropy continuity for interval maps with holes, Ergodic Theory Dynam. Systems, 38 (2018), 2036-2061.
doi: 10.1017/etds.2016.115. |
[4] |
K. Brucks and M. Misiurewicz,
The trajectory of the turning point is dense for almost all tent maps, Ergodic Theory Dynam. Systems, 16 (1996), 1173-1183.
doi: 10.1017/S0143385700009962. |
[5] |
H. Bruin,
For almost every tent map, the turning point is typical, Fund. Math., 155 (1998), 215-235.
|
[6] |
E. M. Coven, I. Kan and J. A. Yorke,
Pseudo-orbit shadowing in the family of tent maps, Trans. Amer. Math. Soc., 308 (1988), 227-241.
doi: 10.1090/S0002-9947-1988-0946440-2. |
[7] |
N. Dobbs and N. Mihalache,
Diabolical entropy, Comm. Math. Phys., 365 (2019), 1091-1123.
doi: 10.1007/s00220-019-03293-y. |
[8] |
M. Keane,
Strongly mixing $g$-measures, Invent. Math., 16 (1972), 309-324.
doi: 10.1007/BF01425715. |
[9] |
G. Keller and C. Liverani, Stability of the spectrum for transfer operators., Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 28 (1999), 141-152, http://www.numdam.org/item/?id=ASNSP_1999_4_28_1_141_0. |
[10] |
F. Ledrappier,
Principe variationnel et systèmes dynamiques symboliques, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 30 (1974), 185-202.
doi: 10.1007/BF00533471. |
[11] |
C. Liverani, B. Saussol and S. Vaienti,
Conformal measure and decay of correlation for covering weighted systems, Ergodic Theory Dynam. Systems, 18 (1998), 1399-1420.
doi: 10.1017/S0143385798118023. |
[12] |
J. Milnor and W. Thurston, On iterated maps of the interval, In Dynamical Systems (College Park, MD, 1986-87), volume 1342 of Lecture Notes in Math., Springer, Berlin, 1988, 465-563.
doi: 10.1007/BFb0082847. |
[13] |
M. Misiurewicz and A. Rodrigues,
Counting preimages, Ergodic Theory Dynam. Systems, 38 (2018), 1837-1856.
doi: 10.1017/etds.2016.103. |
[14] |
H. H. Rugh and L. Tan,
Kneading with weights, J. Fractal Geom., 2 (2015), 339-375.
doi: 10.4171/JFG/24. |
[15] |
G. Tiozzo,
Continuity of core entropy of quadratic polynomials, Invent. Math., 203 (2016), 891-921.
doi: 10.1007/s00222-015-0605-9. |
[16] |
G. Tiozzo,
The local Hölder exponent for the entropy of real unimodal maps, Sci. China Math., 61 (2018), 2299-2310.
doi: 10.1007/s11425-017-9293-7. |
[17] |
P. Walters,
Ruelle's operator theorem and $g$-measures, Trans. Amer. Math. Soc., 214 (1975), 375-387.
doi: 10.2307/1997113. |
show all references
References:
[1] |
V. Baladi, Positive Transfer Operators and Decay of Correlations, volume 16 of Advanced Series in Nonlinear Dynamics, World Scientific Publishing Co., Inc., River Edge, NJ, 2000.
doi: 10.1142/9789812813633. |
[2] |
V. Baladi and D. Ruelle,
An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps, Ergodic Theory Dynam. Systems, 14 (1994), 621-632.
doi: 10.1017/S0143385700008087. |
[3] |
O. F. Bandtlow and H. H. Rugh,
Entropy continuity for interval maps with holes, Ergodic Theory Dynam. Systems, 38 (2018), 2036-2061.
doi: 10.1017/etds.2016.115. |
[4] |
K. Brucks and M. Misiurewicz,
The trajectory of the turning point is dense for almost all tent maps, Ergodic Theory Dynam. Systems, 16 (1996), 1173-1183.
doi: 10.1017/S0143385700009962. |
[5] |
H. Bruin,
For almost every tent map, the turning point is typical, Fund. Math., 155 (1998), 215-235.
|
[6] |
E. M. Coven, I. Kan and J. A. Yorke,
Pseudo-orbit shadowing in the family of tent maps, Trans. Amer. Math. Soc., 308 (1988), 227-241.
doi: 10.1090/S0002-9947-1988-0946440-2. |
[7] |
N. Dobbs and N. Mihalache,
Diabolical entropy, Comm. Math. Phys., 365 (2019), 1091-1123.
doi: 10.1007/s00220-019-03293-y. |
[8] |
M. Keane,
Strongly mixing $g$-measures, Invent. Math., 16 (1972), 309-324.
doi: 10.1007/BF01425715. |
[9] |
G. Keller and C. Liverani, Stability of the spectrum for transfer operators., Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 28 (1999), 141-152, http://www.numdam.org/item/?id=ASNSP_1999_4_28_1_141_0. |
[10] |
F. Ledrappier,
Principe variationnel et systèmes dynamiques symboliques, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 30 (1974), 185-202.
doi: 10.1007/BF00533471. |
[11] |
C. Liverani, B. Saussol and S. Vaienti,
Conformal measure and decay of correlation for covering weighted systems, Ergodic Theory Dynam. Systems, 18 (1998), 1399-1420.
doi: 10.1017/S0143385798118023. |
[12] |
J. Milnor and W. Thurston, On iterated maps of the interval, In Dynamical Systems (College Park, MD, 1986-87), volume 1342 of Lecture Notes in Math., Springer, Berlin, 1988, 465-563.
doi: 10.1007/BFb0082847. |
[13] |
M. Misiurewicz and A. Rodrigues,
Counting preimages, Ergodic Theory Dynam. Systems, 38 (2018), 1837-1856.
doi: 10.1017/etds.2016.103. |
[14] |
H. H. Rugh and L. Tan,
Kneading with weights, J. Fractal Geom., 2 (2015), 339-375.
doi: 10.4171/JFG/24. |
[15] |
G. Tiozzo,
Continuity of core entropy of quadratic polynomials, Invent. Math., 203 (2016), 891-921.
doi: 10.1007/s00222-015-0605-9. |
[16] |
G. Tiozzo,
The local Hölder exponent for the entropy of real unimodal maps, Sci. China Math., 61 (2018), 2299-2310.
doi: 10.1007/s11425-017-9293-7. |
[17] |
P. Walters,
Ruelle's operator theorem and $g$-measures, Trans. Amer. Math. Soc., 214 (1975), 375-387.
doi: 10.2307/1997113. |
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