Escaping Orbits Are also Rare in the Almost Periodic Fermi–Ulam Ping-Pong

Besicovitch, A.S.: On generalized almost periodic functions. Proc. Lond. Math. Soc. s2–25(1), 495–512 (1926)

Biasi, C., Gutierrez, C., dos Santos, E.L.: The implicit function theorem for continuous functions. Topol. Methods Nonlinear Anal. 32(1), 177–185 (2008)

Bell, H., Meyer, K.: Limit periodic functions, adding machines, and solenoids. J. Dyn. Differ. Equat. 7, 409–422 (1995)

Bochner, S.: Beiträge zur Theorie der fastperiodischen Funktionen. Math. Ann. 96(1), 119–147 (1927)

Bohr, H.: Zur Theorie der fast periodischen Funktionen. Acta Math. 45, 29–127 (1925)

Chulaevsky, V.A.: Almost Periodic Operators and Related Nonlinear Integrable Systems. Manchester University Press, Manchester (1989)

Campos, J., Tarallo, M.: Nonmonotone equations with large almost periodic forcing terms. J. Differ. Equ. 254(2), 686–724 (2013)

Dolgopyat, D.: Lectures on Bouncing Balls. https://www.math.umd.edu/~dolgop/BBNotes2.pdf. Online; Accessed 6 Aug 2019

Dolgopyat, D.: Bouncing balls in non-linear potentials. Discrete Contin. Dynam. Syst. 22(1), 165–182 (2008)

Dolgopyat, D.: Geometric and Probabilistic Structures in Dynamics, chapter Fermi acceleration, pp. 149–166. AMS, Providence (2008)

Dolgopyat, D., de Simoi, J.: Dynamics of some piecewise smooth Fermi-Ulam models. Chaos: An Interdisciplinary Journal of Nonlinear Science 22(2), 026124 (2012)

Einsiedler, M., Ward, T.: Ergodic Theory. Springer, London (2011)

Fermi, E.: On the origin of the cosmic radiation. Phys. Rev. 75, 1169–1174 (1949)

Hewitt, E., Ross, K.: Abstract Harmonic Analysis I. Springer, New York (1979)

Kunze, M., Ortega, R.: Complete orbits for twist maps on the plane: extensions and applications. J. Dyn. Differ. Equ. 23(3), 405–423 (2010)

Kunze, M., Ortega, R.: Escaping orbits are rare in the quasi-periodic Fermi-Ulam ping-pong. Ergodic Theory Dyn. Syst. 1-17 (2018)

Laederich, S., Levi, M.: Invariant curves and time-dependent potentials. Ergodic Theory Dyn. Syst. 11(02), (1991)

Moser, J.: On invariant curves of area-preserving mappings of an annulus. Nachr. Akad. Wiss. Göttingen II, 1–20 (1962)

Meyer, K., Sell, G.: Melnikov transforms, bernoulli bundles, and almost periodic perturbations. Trans. Am. Math. Soc. 314, 07 (1989)

Nemytskii, V.V., Stepanov, V.V.: Qualitative Theory of Differential Equations. Princeton Univ Press, Princeton (1960)

Ortega, R., Tarallo, M.: Almost periodic linear differential equations with non-separated solutions. J. Funct. Anal. 237(2), 402–426 (2006)

Pontryagin, L.S.: Topological Groups. Gordon & Breach, New York (1966)

L.D. Pustyl’nikov. On Ulam’s problem. Theor. Math. Phys. 57(1), 1035–1038 (1983)

Schließauf, H.: Escaping orbits are rare in the quasi-periodic Littlewood boundedness problem. Nonlinear Differ. Equ. Appl. NoDEA, 26, (2019)

de Simoi, J.: Fermi acceleration in anti-integrable limits of the standard map. Commun. Math. Phys. 321(3), 703–745 (2013)

Stepanoff, W.: Über einige Verallgemeinerungen der fast periodischen Funktionen. Mathematische Annalen, 95(1), 473–498 (1926)

Ulam, S.M.: On Some Statistical Properties of Dynamical Systems. In: Proceedings of the Fourth Berkeley Symposium on Math. Statistics and Probability, Volume 3: Contributions to Astronomy, Meteorology, and Physics, pp. 315–320. University of California Press, Berkeley (1961)

Weyl, H.: Integralgleichungen und fastperiodische Funktionen. Math. Ann. 97(1), 338–356 (1927)

Zharnitsky, V.: Instability in Fermi–Ulam ping-pong problem. Nonlinearity 11(6), 1481–1487 (1998)

Zharnitsky, V.: Invariant curve theorem for quasiperiodic twist mappings and stability of motion in Fermi–Ulam problem. Nonlinearity 13(4), 1123–1136 (2000)