Weitere Kapitel dieses Buchs durch Wischen aufrufen
Sinai was never really far away from Mathematical Physics. Already his first papers on Kolmogorov–Sinai entropy and on the stability of Kolmogorov’s flow in 2D hydrodynamics (joint with L. Meshalkin, ) were very much in the areas which are closely related to Mathematical Physics. However, in his first research period, roughly in the late 1950s and the early 1960s, Sinai’s work was mostly concentrated around Ergodic Theory and Dynamical Systems. It is fair to say that his deep and lasting interest in Mathematical Physics started with his work on Statistical Mechanics in the late 1960s. This period culminated in the celebrated Pirogov–Sinai theory of phase transitions for ferromagnetic systems. After that Mathematical Physics was always one of the main themes of Sinai’s research. In general it was a period of very active interaction between mathematicians and physicists in the USSR.
Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten
Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:
V.I. Arnold. Small denominators. I. Mapping the circle onto itself (in Russian). Izv. Akad. Nauk SSSR Ser. Mat., 25:21–86, 1961.
P.M. Bleher and Ya.G. Sinai. Critical indices for Dyson’s asymptotically-hierarchical models. Comm. Math. Phys., 45(3):247–278, 1975.
C. Boldrighini and D. Li. Sinai’s dynamical system perspective on mathematical fluid dynamics. In H. Holden, R. Piene, editors, The Abel Prize 2013–2017, pages 175–194. Springer, 2019.
E.I. Dinaburg and Ya.G. Sinai. The one-dimensional Schrödinger equation with a quasiperiodic potential. Funct. Anal. Appl., 9:279–289, 1976.
R. Dobrushin, R. Kotecký, and S. Shlosman. Wulff Construction, volume 104 of Translations of Mathematical Monographs. American Mathematical Society, Providence, RI, 1992.
W. E, K. Khanin, A. Mazel, and Ya. Sinai. Probability distribution functions for the random forced Burgers equation. Phys. Rev. Lett., 78:1904–1907, March 1997.
W. E, K. Khanin, A. Mazel, and Ya. Sinai. Invariant measures for Burgers equation with stochastic forcing. Ann. of Math. (2), 151(3):877–960, 2000.
K.M. Khanin and Ya.G. Sinai. The renormalization group method and the KAM theory. In R.Z. Sagdeev, editor, Nonlinear Phenomena in Plasma Physics and Hydrodynamics, pages 93–118. Mir, Moscow, 1986.
R.A. Minlos and Ya.G. Sinai. The phenomenon of “separation of phases” at low temperatures in certain lattice models of a gas. I. Math. USSR-Sb., 2(3):335–395, 1967. CrossRef
R.A. Minlos and Ya.G. Sinai. The phenomenon of “separation of phases” at low temperatures in certain lattice models of a gas. II. Trans. Moscow Math. Soc., 19:121–196, 1968.
E. Pechersky (guest editor), The European Physical Journal H. Seminar on Mathematical Statistical Physics in Moscow State University, 1962–1994, volume 37(4). Springer, 2012.
Ya.G. Sinai. The limiting behavior of a one-dimensional random walk in a random medium. Theory Probab. Appl., 27:256–268, 1982. CrossRef
Ya.G. Sinai. Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential. J. Statist. Phys., 46(5–6):861–909, 1987.
- Mathematical Physics
Neuer Inhalt/© ITandMEDIA