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Selecta I: Ergodic Theory and Dynamical Systems 2010 ed. [Hardback]

  • Formāts: Hardback, 450 pages, height x width: 260x193 mm, 53 Illustrations, color; 11 Illustrations, black and white; XVI, 450 p. 64 illus., 53 illus. in color. With New printing in a different form., 1 Hardback
  • Izdošanas datums: 23-Aug-2010
  • Izdevniecība: Springer-Verlag New York Inc.
  • ISBN-10: 0387878696
  • ISBN-13: 9780387878690
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  • Formāts: Hardback, 450 pages, height x width: 260x193 mm, 53 Illustrations, color; 11 Illustrations, black and white; XVI, 450 p. 64 illus., 53 illus. in color. With New printing in a different form., 1 Hardback
  • Izdošanas datums: 23-Aug-2010
  • Izdevniecība: Springer-Verlag New York Inc.
  • ISBN-10: 0387878696
  • ISBN-13: 9780387878690
Citas grāmatas par šo tēmu:
The 20 papers in this volume span mathematical physics, dynamical systems, and probability. Yakov Sinai is one of the most important and influential mathematicians of our time; this book will interest researchers from all fields of the physical sciences.

The 20 papers contained in this volume span the areas of mathematical physics, dynamical systems, and probability. Yakov Sinai is one of the most important and influential mathematicians of our time, having won the Boltzmann Medal (1986), the Dirac Medal (1992), Dannie Heinemann Prize for Mathematical Physics (1989), Nemmers Prize (2002), and the Wolf Prize in Mathematics (1997).  He is well-known as both a mathematician and a physicist, with numerous theorems and proofs bearing his name in both fields, and this book should be of interest to researchers from all fields of the physical sciences.

Recenzijas

From the reviews:

The first volume is devoted to ergodic theory and dynamical systems. It contains 19 papers divided into four groups . The reader will find a wealth of information and ideas that can still ignite inspiration and motivate students as well as senior researchers. The reader will also have a touch of Sinais personality, his taste, enthusiasm, and optimism, which are just as invaluable as his mathematical results. (Nikolai Chernov, Mathematical Reviews, Issue 2012 e)

Volume 1 Ergodic Theory and Dynamical Systems
Part I Entropy Theory of Dynamical Systems
1 On the notion of entropy of a dynamical system, Dokl. Akad. Nauk SSSR, 124 (1959), 768-771; Translated by the Author
3(8)
2 Construction and properties of invariant measurable partitions, Dokl. Akad. Nauk. SSSR, 141 (1961), no. 5, 1038-1041; Translated in Soviet Math. Dokl.,, 2 (1961), no. 4-6, 1611-1614
11(5)
V. A. Rokhlin
3 Weak isomorphism of transformations with invariant measure, Mat. Sb. (N.S.). 63 (105) (1964), 23-42; Translated in Amer. Math. Soc. trasl. (2), 57 (1966), 123-149
16(22)
4 Dynamical systems with countably-multiple Lebesgue spectrum. I., Izv. Akad. Nauk SSSR Ser. Mat., 25 (1961), 899-924; Translated in Amer. Math. Soc. transl. (2), 39 (1964), 83-110
38(29)
5 Dynamical systems with countably-multiple lebesgue spectrum. II, Izv. Akad. Nauk SSSR Ser. Mat., 30 (1966), 15-68; Translated in Amer. Math. Soc. transl. (2), 68 (1968), 34-88
67(60)
Part II Ergodic Theory and Number Theory
1 Renewal-type limit theorem for the Gauss map and continued fractions, Ergodic Theory Dyn. Syst., 28 (2008), no. 2, 643-655
127(14)
C. Ulcigrai
2 A Limit Theorem for Birkhoff sums of non-integrable functions over rotations, Contemporary Mathematics, 469 (2008), 317-340
141(25)
C. Ulcigrai
3 Mixing for some classes of special flows over rotations of the circle, Functional. Anal, i Prilozhen., 26 (1992), no. 3, 1-21, Translated in Funct. Anal. Appl., 26 (1992), no. 3, 155-169
166(16)
K. M. Khanin
4 Smoothness of conjugacies of diffeomorphisms of the circle with rotations, Uspekhi Mat. Nauk, 44 (1989), no. 1, 57-82, 247; Translated in Russian Math. Surveys, 44 (1989), no. 1, 66-99
182(31)
K. M. Khanin
5 Feigenbaum universality and the thermodynamic formalism, Uspekhi Mat. Nauk, 39 (1984), no. 3, 3-37; Translated in Russian Math. Surveys, 39 (1984), no. 3, 1-40
213(44)
E. B. Vul
K. M. Khanin
Part III The Theory of Hyperbolic Dynamical Systems: Markov Partitions and Thermodynamic Formalism
1 Markov Partitions and C-diffeomorphisms, Functional. Anal, i Prilozen., 2 (1968), no. 1, 64-89; Translated in Funct. Anal. Appl., 2 (1968), no. 1, 61-82
257(23)
2 Gibbs measures in ergodic theory, Uspekhi Mat. Nauk, 27 (1972), no. 4 (166), 21-64; Translated in Russian Math. Surveys, 27 (1972), no. 4, 21-69
280(48)
3 Gibbs measures for partially hyperbolic attractors, Ergodic Theory and Dyn. Syst., 2 (1982), no. 3-4, 417-438
328(23)
Ya. B. Pesin
4 Steady-state electrical conduction in the periodic Lorentz gas, Comm. Math. Phys., 154 (1993), no. 3, 569-601
351(32)
N. I. Chernov
G. Eyink
J. Lebowitz
5 Space-time chaos in the system of weakly interacting hyperbolic systems, J. Geom. Phys., 5 (1988), no. 3, 483-492
383(14)
Ya. Pesin
Part IV Billiards
1 Dynamical systems with elastic reflections, Uspehi Mat. Nauk, 25 (1970), no. 2 (152), 141-192; Translated in Russian Math. Surveys, 25 (1970), no. 2, 137-189
397(53)
2 On a fundamental theorem in the theory of dispersing billiards, Mat. Sb. (N.S.), 90 (132) (1973), 415-431; Translated in Math. USSR-Sb., 19 (1973), no. 3, 407-423
450(18)
L. A. Bunimovich
3 Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls, Uspekhi Mat. Nauk, 42 (1987), no. 3, 153-174; Translated in Russian Math. Surveys, 42 (1987), no. 3, 181-207
468(26)
N. I. Chernov
4 Billiard trajectories in a polyhedral angle, Uspekhi Mat. Nauk, 33 (1978), no. 1 (199), 229-230; Translated in Russian Math. Surveys, 33 (1978), no. 1, 219-220
494