By Angelo Vulpiani, Roberto Livi

ISBN-10: 3540203079

ISBN-13: 9783540203070

ISBN-10: 3642057861

ISBN-13: 9783642057861

The current quantity, released on the get together of his a hundredth birthday anniversary, is a suite of articles that studies the impression of Kolomogorov's paintings within the actual sciences and gives an advent to the trendy advancements which were prompted during this technique to surround contemporary purposes in biology, chemistry, details sciences and finance.

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The current quantity, released on the social gathering of his a centesimal birthday anniversary, is a suite of articles that studies the impression of Kolomogorov's paintings within the actual sciences and offers an advent to the trendy advancements which have been prompted during this method to surround fresh functions in biology, chemistry, info sciences and finance.

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Nonetheless, Oseledec’s multiplicative theorem [64] guarantees that, under quite general conditions, the following limit exists λ = lim lim t→∞ δr(0)→0 1 δr(t) ln . t δr(0) (19) Accordingly λ can be interpreted as the “average” exponential rate of divergence of nearby trajectories, where the average is made over the portion of phase space accessible to the trajectory (see also (2)). It is worth stressing that this quantity is independent of the choice of the initial conditions, provided they belong to the same chaotic component of the phase space.

Energy Part C: Plasma Phys. 1 253 (1960)] 26. Y. F. Escande, Microscopic dynamics of plasmas and chaos (IOP, Bristol and Philadelphia 2003) 27. V. Chirikov, Proc. R. Soc. London, Ser. A 413, 145 (1987) 28. M. Izrailev, Physica D 1, 243 (1980) 29. G. Casati, I. L. Shepelyansky, IEEE Jour. of Quant. Elect. 24, 1420 (1988) Kolmogorov Pathways from Integrability to Chaos and Beyond 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59.

P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985) 32 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. R. Livi, S, Ruffo, and D. B. Pesin, Russ. Math. Surveys 32, 55 (1977) R. Livi, A. Politi, and S. Ruffo, J. Phys. P. Eckmann and E. Wayne, J. Stat. Phys. G. Sinai, Int. J. Bifur. Chaos, 6, 1137 (1996) S. Tanase-Nicola and J. Kurchan, cond-mat/0302448 G. D. Cohen, J. Stat. Phys. P. Feynman, Found. Phys. A. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge 2000) B.

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