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Analytic skew-products of quadratic polynomials over Misiurewicz-Thurston maps
1. | Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, 119076, Singapore, Singapore |
References:
[1] |
J. F. Alves, A survey of recent results on some statistical features of non-uniformly expanding maps, Discrete Contin. Dyn. Syst., 15 (2006), 1-20.
doi: 10.3934/dcds.2006.15.1. |
[2] |
J. F. Alves, SRB measures for non-hyperbolic systems with multidimensional expansion, Ann. Sci. École Norm. Sup. (4), 33 (2000), 1-32.
doi: 10.1016/S0012-9593(00)00101-4. |
[3] |
J. F. Alves, C. Bonatti and M. Viana, SRB measures for partially hyperbolic systems whose central direction is mostly expanding, Invent. Math., 140 (2000), 351-398.
doi: 10.1007/s002220000057. |
[4] |
J. F. Alves and D. Schnellmann, Ergodic properties of Viana-like maps with singularities in the base dynamics, Proc. Amer. Math. Soc., 141 (2013), 3943-3955.
doi: 10.1090/S0002-9939-2013-11680-1. |
[5] |
J. F. Alves and M. Viana, Statistical stability for robust classes of maps with non-uniform expansion, Ergodic Theory Dynam. Systems, 22 (2002), 1-32.
doi: 10.1017/S0143385702000019. |
[6] |
J. Buzzi, O. Sester and M. Tsujii, Weakly expanding skew-product of quadratic maps, Ergodic Theory Dynam. Systems, 23 (2003), 1401-1414.
doi: 10.1017/S0143385702001694. |
[7] |
L. Carleson and T. W. Gamelin, Complex Dynamics, Universitext: Tracts in Mathematics. Springer-Verlag, New York, 1993. |
[8] |
W. Huang and W. Shen, Analytic skew products of quadratic polynomials over circle expanding maps, Nonlinearity, 26 (2013), 389-404.
doi: 10.1088/0951-7715/26/2/389. |
[9] |
J. Milnor, Dynamics in One Complex Variable, Third Edition, Annals of Mathematics Studies, 160. Princeton University Press, Princeton, NJ, 2006. |
[10] |
T. Nowicki, Symmetric $S$-unimodal mappings and positive Liapunov exponents, Ergodic Theory Dynam. Systems, 5 (1985), 611-616.
doi: 10.1017/S0143385700003199. |
[11] |
D. Schnellmann, Non-continuous weakly expanding skew-products of quadratic maps with two positive Lyapunov exponents, Ergodic Theory Dynam. Systems, 28 (2008), 245-266.
doi: 10.1017/S0143385707000429. |
[12] |
D. Schnellmann, Positive Lyapunov exponents for quadratic skew-products over a Misiurewicz-Thurston map, Nonlinearity, 22 (2009), 2681-2695.
doi: 10.1088/0951-7715/22/11/006. |
[13] |
M. Viana, Multidimensional nonhyperbolic attractors, Inst. Hautes Études Sci. Publ. Math., 85 (1997), 63-96.
doi: 10.1007/BF02699535. |
show all references
References:
[1] |
J. F. Alves, A survey of recent results on some statistical features of non-uniformly expanding maps, Discrete Contin. Dyn. Syst., 15 (2006), 1-20.
doi: 10.3934/dcds.2006.15.1. |
[2] |
J. F. Alves, SRB measures for non-hyperbolic systems with multidimensional expansion, Ann. Sci. École Norm. Sup. (4), 33 (2000), 1-32.
doi: 10.1016/S0012-9593(00)00101-4. |
[3] |
J. F. Alves, C. Bonatti and M. Viana, SRB measures for partially hyperbolic systems whose central direction is mostly expanding, Invent. Math., 140 (2000), 351-398.
doi: 10.1007/s002220000057. |
[4] |
J. F. Alves and D. Schnellmann, Ergodic properties of Viana-like maps with singularities in the base dynamics, Proc. Amer. Math. Soc., 141 (2013), 3943-3955.
doi: 10.1090/S0002-9939-2013-11680-1. |
[5] |
J. F. Alves and M. Viana, Statistical stability for robust classes of maps with non-uniform expansion, Ergodic Theory Dynam. Systems, 22 (2002), 1-32.
doi: 10.1017/S0143385702000019. |
[6] |
J. Buzzi, O. Sester and M. Tsujii, Weakly expanding skew-product of quadratic maps, Ergodic Theory Dynam. Systems, 23 (2003), 1401-1414.
doi: 10.1017/S0143385702001694. |
[7] |
L. Carleson and T. W. Gamelin, Complex Dynamics, Universitext: Tracts in Mathematics. Springer-Verlag, New York, 1993. |
[8] |
W. Huang and W. Shen, Analytic skew products of quadratic polynomials over circle expanding maps, Nonlinearity, 26 (2013), 389-404.
doi: 10.1088/0951-7715/26/2/389. |
[9] |
J. Milnor, Dynamics in One Complex Variable, Third Edition, Annals of Mathematics Studies, 160. Princeton University Press, Princeton, NJ, 2006. |
[10] |
T. Nowicki, Symmetric $S$-unimodal mappings and positive Liapunov exponents, Ergodic Theory Dynam. Systems, 5 (1985), 611-616.
doi: 10.1017/S0143385700003199. |
[11] |
D. Schnellmann, Non-continuous weakly expanding skew-products of quadratic maps with two positive Lyapunov exponents, Ergodic Theory Dynam. Systems, 28 (2008), 245-266.
doi: 10.1017/S0143385707000429. |
[12] |
D. Schnellmann, Positive Lyapunov exponents for quadratic skew-products over a Misiurewicz-Thurston map, Nonlinearity, 22 (2009), 2681-2695.
doi: 10.1088/0951-7715/22/11/006. |
[13] |
M. Viana, Multidimensional nonhyperbolic attractors, Inst. Hautes Études Sci. Publ. Math., 85 (1997), 63-96.
doi: 10.1007/BF02699535. |
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