-
Previous Article
The number of nodal solutions for the Schrödinger–Poisson system under the effect of the weight function
- DCDS Home
- This Issue
-
Next Article
On the dynamics of 3D electrified falling films
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. |
[1] |
Rafael Luís, Sandra Mendonça. A note on global stability in the periodic logistic map. Discrete & Continuous Dynamical Systems - B, 2020, 25 (11) : 4211-4220. doi: 10.3934/dcdsb.2020094 |
[2] |
Charlene Kalle, Niels Langeveld, Marta Maggioni, Sara Munday. Matching for a family of infinite measure continued fraction transformations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (11) : 6309-6330. doi: 10.3934/dcds.2020281 |
[3] |
Elena Bonetti, Pierluigi Colli, Gianni Gilardi. Singular limit of an integrodifferential system related to the entropy balance. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 1935-1953. doi: 10.3934/dcdsb.2014.19.1935 |
[4] |
Wentao Huang, Jianlin Xiang. Soliton solutions for a quasilinear Schrödinger equation with critical exponent. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1309-1333. doi: 10.3934/cpaa.2016.15.1309 |
[5] |
Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006 |
[6] |
Tobias Geiger, Daniel Wachsmuth, Gerd Wachsmuth. Optimal control of ODEs with state suprema. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021012 |
[7] |
Enkhbat Rentsen, Battur Gompil. Generalized Nash equilibrium problem based on malfatti's problem. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 209-220. doi: 10.3934/naco.2020022 |
[8] |
Liangliang Ma. Stability of hydrostatic equilibrium to the 2D fractional Boussinesq equations. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021068 |
[9] |
Manfred Einsiedler, Elon Lindenstrauss. On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method. Journal of Modern Dynamics, 2008, 2 (1) : 83-128. doi: 10.3934/jmd.2008.2.83 |
[10] |
Guirong Jiang, Qishao Lu. The dynamics of a Prey-Predator model with impulsive state feedback control. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1301-1320. doi: 10.3934/dcdsb.2006.6.1301 |
[11] |
Yunfei Lv, Rong Yuan, Yuan He. Wavefronts of a stage structured model with state--dependent delay. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 4931-4954. doi: 10.3934/dcds.2015.35.4931 |
[12] |
Daoyuan Fang, Ting Zhang. Compressible Navier-Stokes equations with vacuum state in one dimension. Communications on Pure & Applied Analysis, 2004, 3 (4) : 675-694. doi: 10.3934/cpaa.2004.3.675 |
[13] |
Pengfei Wang, Mengyi Zhang, Huan Su. Input-to-state stability of infinite-dimensional stochastic nonlinear systems. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021066 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]