Voir la notice de l'article provenant de la source Math-Net.Ru
@article{ND_2010_6_4_a1, author = {Yu. L. Bolotin and S. V. Slipushenko and A. V. Tur and V. V. Yanovsky}, title = {Targeting with external noise}, journal = {Russian journal of nonlinear dynamics}, pages = {719--736}, publisher = {mathdoc}, volume = {6}, number = {4}, year = {2010}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/ND_2010_6_4_a1/} }
TY - JOUR AU - Yu. L. Bolotin AU - S. V. Slipushenko AU - A. V. Tur AU - V. V. Yanovsky TI - Targeting with external noise JO - Russian journal of nonlinear dynamics PY - 2010 SP - 719 EP - 736 VL - 6 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ND_2010_6_4_a1/ LA - ru ID - ND_2010_6_4_a1 ER -
Yu. L. Bolotin; S. V. Slipushenko; A. V. Tur; V. V. Yanovsky. Targeting with external noise. Russian journal of nonlinear dynamics, Tome 6 (2010) no. 4, pp. 719-736. http://geodesic.mathdoc.fr/item/ND_2010_6_4_a1/
[1] Bolotin Yu. L., Tur A. V., Yanovsky V. V., Chaos: Concepts, control and constructive use, Springer, Berlin, 2009, 198 pp. | MR | Zbl
[2] Aubry S., “The new concept of transitions by breaking of analyticity in a crystallographic model”, Solitons and condensed matter physics, Proc. Sympos. Nonlinear (Soliton) Structure and Dynamics in Condensed Matter (Oxford, 1978), Springer Ser. Solid-State Sci., 8, eds. A. R. Bishop and T. Schneider, Springer, Berlin–New York, 1978, 264–277 | MR
[3] Mather J. N., “Existence of quasi-periodic orbits for twist homeomorphisms of the annulus”, Topology, 21 (1982), 457–467 | DOI | MR | Zbl
[4] Kandrup H. E., “Phase space transport in noisy Hamiltonian systems”, Ann. New York Acad. Sci., 867 (1998), 320–333
[5] Ott E., Grebogi C., Yorke J., “Controlling chaos”, Phys. Rev. Lett., 64 (1990), 1196–1199 | DOI | MR | Zbl
[6] Shinbrot T., Grebogi C., Yorke J., “Using chaos to direct trajectories to targets”, Phys. Rev. Lett., 65 (1990), 3215–3218 | DOI
[7] Grebogi C., Ott E., Yorke J., “Critical exponent of chaotic transients in nonlinear dynamical systems”, Phys. Rev. Lett., 57 (1986), 1284–1287 | DOI | MR
[8] Karney C., “Long-time correlations in the stochastic regimes”, Phys. D, 8 (1983), 360–380 | DOI | MR
[9] Schroer C., Ott E., “Targeting in Hamiltonian systems that have mixed regular/chaotic phase spase”, Chaos, 7:4 (1997), 512–519 | DOI | MR | Zbl
[10] Poincaré H., “Sur le probléme des trois corps et les équations de la dynamique”, Acta Math., 13 (1890), 1–270
[11] Feder E., Fraktaly, Mir, M., 1991, 254 pp.
[12] Anischenko V. S., Neiman A. B., “Period vozvrata Puankare v rezhime dinamicheskogo khaosa”, ZhTF, 59:8 (1989), 117–118
[13] Boshernitzan M., “Quantitative recurrence results”, Invent. Math., 113:3 (1993), 617–631 | DOI | MR | Zbl
[14] Saussol B., Troubetzkoy S., Vaienti S., “Recurrence, dimensions and Lyapunov exponents”, J. Stat. Phys., 106 (2002), 623–634 | DOI | MR | Zbl
[15] Kim C., Kim D. H., “On the law of logarithm of the recurrence time”, Discrete Contin. Dyn. Sys., 10:3 (2004), 581–587 | DOI | MR | Zbl
[16] Haydn N., Luevano J., Mantica G., Vaienti S., “Multifractal properties of return time statistics”, Phys. Rev. Lett., 88 (2002), 224502, 4 pp. | DOI
[17] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 1, Mir, M., 1984, 511 pp.
[18] Zaslavsky G. M., Edelman M., Niyazov B. A., “Self-similarity, renormalization, and phase space nonuniformity of Hamiltonian chaotic dynamics”, Chaos, 7:1 (1997), 159–181 | DOI | MR | Zbl
[19] Kac M., Probability and related topics in physical sciences, Interscience, New York, 1959, 266 pp. | MR | Zbl
[20] Hénon M., “A two-dimensional mapping with a strange attractor”, Commun. Math. Phys., 50:1 (1976), 69–77 | DOI | MR
[21] Kaplan H., “Return to type-I intermittency”, Phys. Rev. Lett., 68 (1992), 553–556 | DOI | MR | Zbl
[22] Kaplan H., “Type-I intermittency for the Hénon-map family”, Phys. Rev. E, 48 (1993), 1655–1669 | DOI | MR
[23] Rodrigues Ch. S., Grebogi C., de Moura A. P. S., Escape from attracting sets in randomly perturbed systems, April 2010, arXiv: 1004.3125
[24] Anischenko V. S., Znakomstvo s nelineinoi dinamikoi, URSS, M., 2007, 143 pp.
[25] Klyatskin V. I., Stokhasticheskie uravneniya i volny v sluchaino-neodnorodnykh sredakh, Nauka, M., 1980, 336 pp.
[26] Smale S., “Diffeomorphisms with many periodic points”, Differential and combinatorial topology, ed. S. S. Cairns, Princeton Univ. Press, Princeton, 1965, 63–80 | MR | Zbl
[27] Kuznetsov S. P., Dinamicheskii khaos, Fizmatlit, M., 2001, 294 pp.
[28] Shuster G., Determinirovannyi khaos, Mir, M., 1988, 240 pp.
[29] Hirsch H., Huberman B. A., Scalapino D. J., “Theory of intermittency”, Phys. Rev. A, 25 (1982), 519–532 | DOI