@article{AIHPA_1998__68_4_491_0, author = {Guarneri, Italo}, title = {On the dynamical meaning of spectral dimensions}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {491--506}, publisher = {Gauthier-Villars}, volume = {68}, number = {4}, year = {1998}, mrnumber = {1634313}, zbl = {0910.58031}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1998__68_4_491_0/} }
Guarneri, Italo. On the dynamical meaning of spectral dimensions. Annales de l'I.H.P. Physique théorique, Tome 68 (1998) no. 4, pp. 491-506. http://archive.numdam.org/item/AIHPA_1998__68_4_491_0/
[1] Stochastic Behavior in Classical and Quantum Hamiltonian Systems, G. CSATI and J. FORD eds., Springer Lecture Notes in Physics 93 (1973). | MR
, , and , in[2] Phys. Rev. Lett. 49 (1982) 509. For a review of dynamical localization theory see, e.g., , in Proceedings of the 1991 Varenna Course CXIX, G. CASATI, I. GUARNERI and U. SMILANSKY eds., North-Holland 1993, p.187. | MR
, D , and ,[3] Sov.Sci.Rev., Sect.C, 2, (1981),209. | MR | Zbl
, and ,[4] Europhys.Lett. 10 (1989) 95.
,[5] An early discussion of singular continuous spectra in the context of quantum-classical instabilities appears in Trends and Developments in the Eighties, S.Albeverio and P.Blanchard eds., World Scientific, Singapore (1985).
, in[6] Comm.Math.Phys. 95 (1984) 121. | MR | Zbl
and ,[7] Annals of Math. 141 (1995) 131. | MR
,[8] Phys.Rev.Lett. 67 (1991) 1377; , and , ibid. 67 (1991) 3635; , , and , ibid. 68 (1992) 3826; , , , and , ibid. 69 (1992) 3302.
and ,[9] Phys.Rev. B (1996).
and ,[10] Cond-Mat/9709054 (1997).
, and , preprint[11] Phys. Rev.Lett. 69 (1992) 695; , Commun.Math.Phys. 160 (1994) 457; , , and , report CPT-96/P.3303, Marseille, 1996.
, , and ,[12] Differential Equations with applications to Mathematical Physics, edited by W. F. AMES, E. M. HARREL and J. V. HEROD (Academic, Boston 1993). | MR
, in[13] J.Funct.Anal. 142 (1995) 406. | MR | Zbl
,[14] J.Funct.Anal. 89 (1990) 154. | MR | Zbl
,[15] Phys.Rev. B50, (1994) 1420.
and ,[16] private communication.
,[17] Como 1998.
and , preprint,[18] Phys. Rev. Lett. 76 (1996) 4372.
,[19] Physica D 109 (1997) 113. | Zbl
,[20] J.Phys. (Cond. Matter) 7 (1995) 3507.
, , and ,[21] Lectures on Ergodic Theory, Chelsea (1956); , , and , Ergodic Theory, vol. 115 of Grundlehren der matematischen Wissenschaften in Einzeldarstellungen, Springer (1982). A review of classical "genericity" results in the light of recent results in abstract operator theory is given by , Discr. Cont. Dynamical Systems 4 (1998) 33. | MR | Zbl
,[22] Substitution Dynamical Systems - Spectral Analysis, Springer Lecture Notes in Mathematics 1294 (1987). | MR | Zbl
,[23] Physica D 19 (1986) 311, and references therein. | MR | Zbl
,[24] Phys.Rev.E.
, and , to appear in[25] Phys. Rev. E 51 (1995) 1762; and , J.Phys. A: Math. Gen. 28 (1995) 2717, and references therein.
, and ,[26] J.Math.Phys. 37, 10 (1996) 5195. | MR | Zbl
,[27] Phys.Rev.Lett. 79 (1997) 1959. | MR | Zbl
, , , and ,[28] J. d'Analyse Mathématique, 69 (1996) 153. | Zbl
, , and ,