Besicovitch, A.S.: Almost Periodic Functions. Dover Publications, New York (1954)
Bohr, H.: Almost Periodic Functions. Chelsea, New York (1956)
Carmona, R., Lacroix, J.: Spectral Theory of Random Schrödinger Operators. Probability and its Applications. Birkhäuser, Boston (1990)
Chen, B., Dai, X.: On uniformly recurrent motions of topological semigroup actions. Discrete Contin. Dyn. Syst. 36, 2931–2944 (2016)
Damanik, D.: Schrödinger operators with dynamically defined potentials. Ergod. Theory Dyn. Syst. 37, 1681–1764 (2017)
Damanik, D., Fillman, J.: Gap labelling for discrete one-dimensional ergodic Schrödinger operators. In: From Complex Analysis to Operator Theory: A Panorama, Operator Theory: Advances and Applications, vol. 291, pp. 341–404. Birkhäuser/Springer, Cham (2023)
Damanik, D., Zhou, Z.: The rotation number for the almost periodic Schrödinger operator with \(\delta \)-potentials. J. Dyn. Differ. Equ. 34, 155–177 (2022)
Dieudonné, J.: Foundations of Modern Analysis. Academic Press, New York (1969)
Fink, A.: Almost Periodic Differential Equations. Springer, Berlin (1974)
Gottschalk, W.H.: Almost periodicity, equi-continuity and total boundedness. Bull. Am. Math. Soc. 52, 633–636 (1946)
Article MathSciNet Google Scholar
Gottschalk, W.H.: Almost periodic points with respect to transformation semi-groups. Ann. Math. (2) 47, 762–766 (1946)
Article MathSciNet Google Scholar
Hale, J.K.: Ordinary Differential Equations, 2nd edn. Wiley, New York (1980)
Johnson, R.: Exponential dichotomy, rotation number, and linear differential operators with bounded coefficients. J. Differ. Equ. 61, 54–78 (1986)
Article ADS MathSciNet Google Scholar
Johnson, R., Moser, J.: The rotation number for almost periodic potentials. Commun. Math. Phys. 84, 403–438 (1982)
Article ADS MathSciNet Google Scholar
Karpeshina, Y., Parnovski, L., Shterenberg, R.: Bethe-Sommerfeld conjecture and absolutely continuous spectrum of multi-dimensional quasi-periodic Schrödinger operators. arXiv:2010.05881
Kellendonk, J., Lenz, D.: Equicontinuous Delone dynamical systems. Canad. J. Math. 65, 149–170 (2013)
Article MathSciNet Google Scholar
Kelley, J.L.: General Topology. D. Van Nostrand Company Inc, Toronto (1955)
Lee, J., Lenz, D., Richard, C., Sing, B., Strungaru, N.: Modulated crystals and almost periodic measures. Lett. Math. Phys. 110(12), 3435–3472 (2020)
Article ADS MathSciNet Google Scholar
Lenz, D., Stollmann, P.: An ergodic theorem for Delone dynamical systems and existence of the integrated density of states. J. Anal. Math. 97, 1–24 (2005)
Article MathSciNet Google Scholar
Lenz, D., Strungaru, N.: On weakly almost periodic measures. Trans. Am. Math. Soc. 371, 6843–6881 (2019)
Article MathSciNet Google Scholar
Levitan, B.M., Zhikov, V.V.: Almost Periodic Functions and Differential Equations. Cambridge University Press, Cambridge (1982)
Long, Y.: Index Theory for Symplectic Paths with Applications. Birkhäuser, Basel (2002)
Meng, G., Zhang, M.: Dependence of solutions and eigenvalues of measure differential equations on measures. J. Differ. Equ. 254, 2196–2232 (2013)
Article ADS MathSciNet Google Scholar
Pastur, A.L., Figotin, A.: Spectra of Random and Almost-Periodic Operators. Springer, Berlin (1992)
Qi, L., Yuan, R.: A generalization of Bochner’s theorem and its applications in the study of impulsive differential equations. J. Dyn. Differ. Equ. 31, 1955–1985 (2019)
Article MathSciNet Google Scholar
Samoilenko, A.M., Perestyuk, N.A.: Impulsive differential equations, with a supplement by S. I. Trofimchuk. In: World Scientific Series on Nonlinear Science Series A, vol. 14. World Scientific Publishing Co., Inc., River Edge, NJ (1995)
Seifert, C.: Measure-perturbed one-dimensional Schrödinger operators—A continuum model for quasicrystals. Doctoral Dissertation Thesis, Chemnitz University of Technology (2012)
Sell, G.R.: Compact sets of nonlinear operators. Funkcial. Ekvac. 11, 131–138 (1968)
Shen, W., Yi, Y.: Almost automorphic and almost periodic dynamics in skew-product semiflows. Mem. Am. Math. Soc. 136, 647 (1998)
Walters, P.: An Introduction to Ergodic Theory. Springer, Berlin (1982)
Zhang, M.: From almost periodic functions to measures: a unified dynamics approach
Zhang, M., Zhou, Z.: Uniform ergodic theorems for discontinuous skew-product flows and applications to Schrödinger equations. Nonlinearity 24, 1539–1564 (2011)
Article ADS MathSciNet Google Scholar
Zhou, Z.: The rotation number of the linear Schrödinger equation with discontinuous almost periodic potentials. J. Differ. Equ. 259, 4202–4228 (2015)
Comments (0)