Anqie entropy and arithmetic compactification of natural numbers
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Abdalaoui, E..H.. El., Kułaga-Przymus, J., Lemańczyk, M., de La Rue, T.: The Chowla and the Sarnak conjectures from ergodic theory point of view. Discrete Contin. Dyn. Syst. 37, 2899–2944 (2017)
Adler, R.L., Konheim, A.G., McAndrew, M.H.: Topological entropy. Trans. Am. Math. Soc. 114, 309–319 (1965)
Blackadar, B.: K-Theory for Operator Algebras. Mathematical Sciences Research Institute Publications, vol. 5. Cambridge University Press, Cambridge (1998)
Block, L.S., Coppel, W.A.: Dynamics in One Dimension. Lecture Notes in Mathematics, vol. 1513. Springer, Berlin (1992)
Bowen, R.: Entropy for group endomorphisms and homogeneous spaces. Trans. Am. Math. Soc. 153, 401–414 (1971)
Conway, J.H.: A Course in Functional Analysis. Graduate Texts in Mathematics, vol. 96. Springer, New York (1990)
Elliott, G.A.: On the classification of inductive limits of sequences of semisimple finite-dimensional algebras. J. Algebra 38, 29–44 (1976)
Furstenberg, H.: Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation. Math. Syst. Theory 1, 1–49 (1961)
Ge, L.: Topology of natural numbers and entropy of arithmetic functions. In: Operator Algebras and Their Applications: A Tribute to Richard V. Kadison, Contemporary Mathematics, vol. 671, pp. 127–144. American Mathematical Society, Providence (2016)
Glasner, E.: Ergodic Theory via Joinings. Mathematical Surveys and Monographs, vol. 101. American Mathematical Society, Providence (2002)
Iwaniec, H., Kowalski, E.: Analytic Number Theory. American Mathematical Society Colloquium Publications, vol. 53. American Mathematical Society, Providence (2004)
Kadison, R., Ringrose, J.: Fundamentals of the Operator Algebras, Volume I and II. Graduate Studies in Mathematics, vol. 15 and vol. 16, Academic Press, Orlando (1983) and (1986)
Katok, A.: Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Publ. Math. Inst. Hautes Études Sci. 51, 137–173 (1980)
Kolmogorov, A.N.: New metric invariant of transitive dynamical systems and endomorphisms of Lebesgue spaces. Dokl. Russ. Acad. Sci. 119, 861–864 (1958)
Lin, H.: Classification of homomorphisms and dynamical systems, (English summary). Trans. Am. Math. Soc. 359, 859–895 (2007)
Liu, J., Sarnak, P.: The Möbius function and distal flows. Duke Math. J. 164, 1353–1399 (2015)
Murty, M.R.: Problems in Analytic Number Theory. Graduate Texts in Mathematics, vol. 206. Springer, New York (2008)
Pimsner, M., Voiculescu, D.: $$K$$-groups of reduced crossed products by free groups. J. Oper. Theory 8, 131–156 (1982)
Rørdam, M., Larsen, F., Laustsen, N.J.: An Introduction to K-Theory for C*-Algebras. London Mathematical Society Student Texts, vol. 49. Cambridge University Press, Cambridge (2000)
Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(379–423), 623–656 (1948)
Sinai, Y.G.: On the notion of entropy of a dynamical system. Dokl. Russ. Acad. Sci. 124, 768–771 (1959)
Voiculescu, D.: The analogues of entropy and of Fisher’s information measure in free probability theory. Commun. Math. Phys. 155, 71–92 (1993)
Walters, P.: An Introduction to Ergodic Theory. Graduate Texts in Mathematics, vol. 79. Springer, New York (1982)
Wei, F.: Disjointness of Möbius from asymptotically periodic functions. arXiv:1810.07360 (2018)
Ye, X., Huang, W., Shao, S.: An Introduction to Topological Dynamical Systems (in Chinese). Modern Mathematics Foundation Series, vol. 118. Science Press, Beijing (2008)