Decay of Geometry for Fibonacci Critical Covering Maps of the Circle
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 4, pp. 1533-1551.
@article{AIHPC_2009__26_4_1533_0,
     author = {Colli, Eduardo and Do Nascimento, Marcio L. and Vargas, Edson},
     title = {Decay of {Geometry} for {Fibonacci} {Critical} {Covering} {Maps} of the {Circle}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1533--1551},
     publisher = {Elsevier},
     volume = {26},
     number = {4},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.03.001},
     zbl = {1173.37040},
     mrnumber = {2542736},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.03.001/}
}
TY  - JOUR
AU  - Colli, Eduardo
AU  - Do Nascimento, Marcio L.
AU  - Vargas, Edson
TI  - Decay of Geometry for Fibonacci Critical Covering Maps of the Circle
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
DA  - 2009///
SP  - 1533
EP  - 1551
VL  - 26
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2009.03.001/
UR  - https://zbmath.org/?q=an%3A1173.37040
UR  - https://www.ams.org/mathscinet-getitem?mr=2542736
UR  - https://doi.org/10.1016/j.anihpc.2009.03.001
DO  - 10.1016/j.anihpc.2009.03.001
LA  - en
ID  - AIHPC_2009__26_4_1533_0
ER  - 
%0 Journal Article
%A Colli, Eduardo
%A Do Nascimento, Marcio L.
%A Vargas, Edson
%T Decay of Geometry for Fibonacci Critical Covering Maps of the Circle
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 1533-1551
%V 26
%N 4
%I Elsevier
%U https://doi.org/10.1016/j.anihpc.2009.03.001
%R 10.1016/j.anihpc.2009.03.001
%G en
%F AIHPC_2009__26_4_1533_0
Colli, Eduardo; Do Nascimento, Marcio L.; Vargas, Edson. Decay of Geometry for Fibonacci Critical Covering Maps of the Circle. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 4, pp. 1533-1551. doi : 10.1016/j.anihpc.2009.03.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.03.001/

[1] Bruin H., Keller G., Nowicki T., Van Strien S., Wild Cantor Attractors Exist, Ann. of Math. (2) 143 (1996) 97-130. | MR | Zbl

[2] Bruin H., Van Strien S., Existence of Absolutely Continuous Invariant Probability Measures for Multimodal Maps, in: Global Analysis of Dynamical Systems, Inst. Phys., Bristol, 2001, pp. 433-447, 17 (4) (2004) 749-782 (electronic). | MR

[3] Bruin H., Letelier J. R., Shen W., Van Strien S., Large Derivatives, Backward Contraction and Invariant Densities for Interval Maps, Invent. Math. 172 (3) (2008) 509-533. | MR | Zbl

[4] Collet P., Eckmann J. P., Iterated Maps on the Interval as Dynamical Systems, Prog. Phys., vol. 1, Birkhäuser Boston, Massachusetts, 1980. | MR | Zbl

[5] Collet P., Eckmann J. P., Positive Liapunov Exponents and Absolute Continuity for Maps of the Interval, Ergodic Theory Dynam. Systems 3 (1) (1983) 13-46. | MR | Zbl

[6] De Melo W., Van Strien S., One-Dimensional Dynamics, Springer-Verlag, Berlin, 1993. | MR | Zbl

[7] Graczyk J., Świa̧Tek G., Induced Expansions for Quadratic Polynomials, Ann. Sci. École Norm. Sup. (4) (1996) 399-482. | EuDML | Numdam | MR | Zbl

[8] Graczyk J., Świa̧Tek G., Generic Hyperbolicity in the Logistic Family, Ann. of Math. (2) (1997) 1-52. | MR | Zbl

[9] Graczyk J., Świa̧Tek G., The Real Fatou Conjecture, Ann. of Math. Stud., vol. 144, Princeton University Press, Princeton, 1998. | MR | Zbl

[10] Graczyk J., Sands D., Świa̧Tek G., Metric Attractors for Smooth Unimodal Maps, Ann. of Math. (2) 159 (2) (2004) 725-740. | MR | Zbl

[11] Graczyk J., Sands D., Świa̧Tek G., Decay of Geometry for Unimodal Maps: Negative Schwarzian Case, Ann. of Math. (2) 161 (2) (2005) 613-677. | MR | Zbl

[12] Guckenheimer J., Sensitive Dependence to Initial Conditions for One-Dimensional Maps, Comm. Math. Phys. 70 (2) (1979) 133-160. | MR | Zbl

[13] Guckenheimer J., Johnson S., Distortion of S-Unimodal Maps, Ann. of Math. (2) 132 (1) (1990) 71-130. | MR | Zbl

[14] Hofbauer F., Keller G., Some Remarks on Recent Results About S-Unimodal Maps, Ann. Inst. H. Poincaré Phys. Théor. 53 (4) (1990) 413-425. | Numdam | MR | Zbl

[15] Jakobson M. V., Absolutely Continuous Invariant Measures for One-Parameter Families of One-Dimensional Maps, Comm. Math. Phys. 81 (1) (1981) 39-88. | MR | Zbl

[16] Jakobson M. V., Świa̧Tek G., Metric Properties of Non-Renormalizable S-Unimodal Maps I. Induced Expansion and Invariant Measures, Ergodic Theory Dynam. Systems 14 (4) (1994) 721-755. | MR | Zbl

[17] Keller G., Nowicki T., Fibonacci Maps Re(Al)Visited, Ergodic Theory Dynam. Systems 15 (1) (1995) 99-120. | MR | Zbl

[18] Krzyzewski K., Slenk W., On Invariant Measures for Expanding Differentiable Mappings, Studia Math. 3 (1969) 83-92. | MR | Zbl

[19] Lasota A., Yorke J. A., On the Existence of Invariant Measures for Piecewise Monotonic Transformations, Trans. Amer. Math. Soc. 186 (1974) 481-488, (1973). | MR | Zbl

[20] Levin G., Bounds for Maps of the Interval With One Reflecting Critical Point I, Fund. Math. 157 (2-3) (1998) 287-298. | MR | Zbl

[21] Levin G., Van Strien S., Bounds for Maps of an Interval With One Critical Point of Inflection Type. II, Invent. Math. 141 (2) (2000) 399-465. | MR | Zbl

[22] Levin G., Świa̧Tek G., Universality of Critical Circle Covers, Comm. Math. Phys. 228 (2002) 371-399. | MR | Zbl

[23] Lyubich M., Combinatorics, Geometry and Attractors of Quasi-Quadratic Maps, Ann. of Math. (2) 140 (2) (1994) 347-404. | MR | Zbl

[24] Lyubich M., Milnor J., The Fibonacci Unimodal Map, J. Amer. Math. Soc. 6 (2) (1993) 425-457. | MR | Zbl

[25] Lyubich M., Dynamics of Quadratic Polynomials. I, II, Acta Math. 178 (2) (1997) 185-247, 247-297. | MR | Zbl

[26] Martens M., Distortion Results and Invariant Cantor Sets of Unimodal Maps, Ergodic Theory Dynam. Systems 14 (2) (1994) 331-349. | MR | Zbl

[27] Martens M., Nowicki T., Invariant Measures for Typical Quadratic Maps, Astérisque 261 (2000) 239-252, xiii. | MR | Zbl

[28] Milnor J., On the Concept of Attractor, Comm. Math. Phys. 99 (2) (1985) 177-195. | MR | Zbl

[29] Misiurewicz M., Absolutely Continuous Measures for Certain Maps of an Interval, Inst. Hautes Études Sci. Publ. Math. 53 (1981) 17-51. | Numdam | MR | Zbl

[30] Misiurewicz M., Rodrigues A., Double Standard Maps, Comm. Math. Phys. 273 (1) (2007) 37-65. | MR | Zbl

[31] Nowicki T., Van Strien S., Invariant Measures Exist Under a Summability Condition for Unimodal Maps, Invent. Math. 105 (1) (1991) 123-136. | MR | Zbl

[32] Ruelle D., Applications Conservant Une Mesure Absolument Continue Par Raport À Dx Sur [0,1], Comm. Math. Phys. 55 (1) (1977) 47-51. | MR | Zbl

[33] Shen W., Decay of Geometry for Unimodal Maps: an Elementary Proof, Ann. of Math. (2) 163 (2) (2006) 383-404. | MR | Zbl

[34] Van Strien S., Hyperbolicity and Invariant Measures for General C 2 Interval Maps Satisfying the Misiurewicz Condition, Comm. Math. Phys. 128 (3) (1990) 437-495. | MR | Zbl

[35] Van Strien S., Vargas E., Real Bounds, Ergodicity and Negative Schwarzian for Multimodal Maps, J. Amer. Math. Soc. 17 (4) (2004) 749-782, (electronic). | MR | Zbl

Cited by Sources: