Asymptotic scaling and universality for skew products with factors in SL(2, $\boldsymbol {\mathbb {R}}$ )
暂无分享,去创建一个
[1] L. H. Eliasson,et al. Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation , 1992 .
[2] On trigonometric skew-products over irrational circle-rotations , 2020, 2004.03102.
[3] M. Lyubich. Feigenbaum-Coullet-Tresser universality and Milnor's hairiness conjecture. , 1999, math/9903201.
[4] H. Koch. On hyperbolicity in the renormalization of near-critical area-preserving maps , 2016 .
[5] I. Satija. A tale of two fractals: The Hofstadter butterfly and the integral Apollonian gaskets , 2016, 1606.09119.
[6] A. Avila,et al. The Ten Martini Problem , 2009 .
[7] Valery Oseledets,et al. Oseledets theorem , 2008, Scholarpedia.
[8] Jean-Pierre Eckmann,et al. A complete proof of the Feigenbaum conjectures , 1987 .
[9] Renormalization in the Hénon Family, I: Universality But Non-Rigidity , 2005, math/0508477.
[10] B. Simon,et al. Duality and singular continuous spectrum in the almost Mathieu equation , 1997 .
[11] H. Koch. Golden mean renormalization for the almost Mathieu operator and related skew products , 2019, Journal of Mathematical Physics.
[12] Golden mean renormalization for a generalized Harper equation: The strong coupling fixed point , 2000 .
[13] T. Johnson,et al. Dynamics of the universal area-preserving map associated with period doubling: hyperbolic sets , 2009, 0905.1390.
[14] Alex Furman,et al. On the multiplicative ergodic theorem for uniquely ergodic systems , 1997 .
[15] Svetlana Ya. Jitomirskaya. Metal-insulator transition for the almost Mathieu operator , 1999 .
[16] B. Simon,et al. Almost periodic Schrödinger operators II. The integrated density of states , 1983 .
[17] Fine Properties of the Integrated Density of States and a Quantitative Separation Property of the Dirichlet Eigenvalues , 2005, math-ph/0501005.
[18] Leo P. Kadanoff,et al. Scaling for a Critical Kolmogorov-Arnold-Moser Trajectory , 1981 .
[19] M. Wilkinson,et al. Nests and chains of Hofstadter butterflies , 2019, Journal of Physics A: Mathematical and Theoretical.
[20] B. Simon,et al. Almost periodic Schrödinger operators , 1981 .
[21] Y. Last. Zero measure spectrum for the almost Mathieu operator , 1994 .
[22] Tsuyoshi Murata,et al. {m , 1934, ACML.
[23] S. Swierczkowski. On successive settings of an arc on the circumference of a circle , 1958 .
[24] H. Koch,et al. The Critical Renormalization Fixed Point for Commuting Pairs of Area-Preserving Maps , 2010 .
[25] J. Palis,et al. Geometric theory of dynamical systems : an introduction , 1984 .
[26] J. Eckmann,et al. A computer-assisted proof of universality for area-preserving maps , 1984 .
[27] J. Avron,et al. Hofstadter butterfly as quantum phase diagram , 2001, math-ph/0101019.
[28] B. Simon,et al. Cantor spectrum for the almost Mathieu equation , 1982 .
[29] D. Thouless,et al. Quantized Hall conductance in a two-dimensional periodic potential , 1992 .
[30] Hofstadter rules and generalized dimensions of the spectrum of Harper's equation , 1996, cond-mat/9610177.
[31] Michael Yampolsky,et al. Hyperbolicity of renormalization of critical circle maps , 2003 .
[32] W. Kyner. Invariant Manifolds , 1961 .
[33] R. Kashaev,et al. Generalized Bethe ansatz equations for Hofstadter problem , 1993, hep-th/9312133.
[34] J. Moser,et al. The rotation number for almost periodic potentials , 1983 .
[35] A. Avila. The absolutely continuous spectrum of the almost Mathieu operator , 2008, 0810.2965.
[36] A. Avila,et al. Monotonic cocycles , 2013, 1310.0703.
[37] A. Avila. Global theory of one-frequency Schrödinger operators , 2015 .
[38] D. Hofstadter. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields , 1976 .
[39] P. G. Harper,et al. Single Band Motion of Conduction Electrons in a Uniform Magnetic Field , 1955 .
[40] C. McMullen. Renormalization and 3-Manifolds Which Fiber over the Circle , 1996 .
[41] Robert S. MacKay,et al. Renormalisation in Area-Preserving Maps , 1993 .
[42] M. Feigenbaum. Quantitative universality for a class of nonlinear transformations , 1978 .
[43] H. Koch,et al. Renormalization and universality of the Hofstadter spectrum , 2019, Nonlinearity.
[44] Pierre Coullet,et al. ITÉRATIONS D'ENDOMORPHISMES ET GROUPE DE RENORMALISATION , 1978 .
[45] A. Avila,et al. Almost localization and almost reducibility , 2008, 0805.1761.