×

zbMATH — the first resource for mathematics

Topological analysis of chaotic dynamical systems. (English) Zbl 1205.37002
Editorial remark: No review copy delivered.

MSC:
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abarbanel, H. D. I., Rev. Mod. Phys. 65 pp 1331– (1993)
[2] Abraham, N. B., J. Opt. Soc. Am. B 2 pp 23– (1985)
[3] Alligood, K. T., Trans. Am. Math. Soc. 292 pp 713– (1985)
[4] Arecchi, F. T., Phys. Rev. Lett. 49 pp 1217– (1982)
[5] Argoul, F., Acc. Chem. Res. 86 pp 119– (1987)
[6] Arnol’d, V. I., Russian Math. Surveys 23 pp 1– (1968) · Zbl 0167.21702
[7] Arnol’d, V. I., Russian Math. Surveys 30 pp 1– (1975) · Zbl 0343.58001
[8] Auerbach, D., Phys. Rev. Lett. 58 pp 2387– (1987)
[9] Beiersdorfer, P., Phys. Lett. A 96 pp 269– (1983)
[10] Bestvina, M., Ann. Math. 135 pp 1– (1992) · Zbl 0757.57004
[11] Birman, J. S., Topology 22 pp 47– (1983) · Zbl 0507.58038
[12] Birman, J. S., Contemp. Math. 20 pp 1– (1983)
[13] Bocko, M. F., Phys. Lett. A 104 pp 388– (1984)
[14] Boulant, G., Phys. Rev. E 55 pp R3801– (1997)
[15] Boulant, G., Phys. Rev. E 55 pp 5208– (1997)
[16] Broomhead, D. S., Physica D 20 pp 217– (1986) · Zbl 0603.58040
[17] Brown, R., Phys. Rev. E 49 pp 3784– (1994)
[18] Chauve, M. P., Physica D 58 pp 407– (1992)
[19] Coffman, K., J. Chem. Phys. 86 pp 119– (1987)
[20] Creveling, H. F., J. Fluid Mech. 67 pp 65– (1975) · Zbl 0312.76029
[21] Cvitanovic, P., Phys. Rev. A 38 pp 1503– (1988)
[22] Dangoisse, D., Europhys. Lett. 6 pp 335– (1988)
[23] Devaney, R., Commun. Math. Phys. 67 pp 137– (1979) · Zbl 0414.58028
[24] Dupertuis, M. A., Opt. Commun. 57 pp 410– (1986)
[25] Eckmann, J.-P., Rev. Mod. Phys. 57 pp 617– (1985) · Zbl 0989.37516
[26] Eckmann, J.-P., Europhys. Lett. 4 pp 973– (1987)
[27] Efron, B., SIAM (Soc. Ind. Appl. Math.) Rev. 21 pp 460– (1979)
[28] Englisch, V., Phys. Rev. A 44 pp 916– (1991)
[29] Eschenazi, E., Phys. Rev. A 39 pp 2609– (1989)
[30] Feigenbaum, M. J., J. Stat. Phys. 19 pp 25– (1978) · Zbl 0509.58037
[31] Feigenbaum, M. J., Los Alamos Sci. 1 pp 4– (1980)
[32] Franks, J., Trans. Am. Math. Soc. 20 pp 241– (1985)
[33] Fujisaka, H., Prog. Theor. Phys. 69 pp 32– (1983) · Zbl 1171.70306
[34] Gilmore, C., Int. J. Bifurcation Chaos Appl. Sci. Eng. 3 pp 583– (1993) · Zbl 0870.58056
[35] Gilmore, C., J. Econ. Behav. Organ. 22 pp 209– (1993)
[36] Gilmore, R., Phys. Rev. E 51 pp 935– (1995)
[37] Gilmore, R., Phys. Rev. E 55 pp 2479– (1997)
[38] Gioggia, R. S., Phys. Rev. Lett. 51 pp 650– (1983)
[39] Gorman, M., Phys. Rev. Lett. 52 pp 2241– (1984)
[40] Gorman, M., Physica D 19 pp 255– (1986) · Zbl 0588.76094
[41] Grassberger, P., Phys. Rev. A 28 pp 2591– (1983)
[42] Grebogi, C., Physica D 7 pp 181– (1983) · Zbl 0561.58029
[43] Gunaratne, G. H., Phys. Rev. Lett. 63 pp 1– (1989)
[44] Haken, H., Phys. Lett. A 53 pp 77– (1975)
[45] Hall, T., Phys. Rev. Lett. 71 pp 58– (1993)
[46] Hall, T., Nonlinearity 7 pp 367– (1994) · Zbl 0913.58048
[47] Hall, T., Nonlinearity 7 pp 861– (1994) · Zbl 0806.58015
[48] Halsey, T. C., Phys. Rev. A 33 pp 1141– (1986) · Zbl 1184.37028
[49] Hammel, S., Phys. Lett. A 148 pp 421– (1990)
[50] Harrison, R. G., IEEE J. Quantum Electron. 21 pp 1491– (1985)
[51] Harrison, R. G., Phys. Rev. Lett. 55 pp 63– (1985)
[52] Hennequin, D., Phys. Rev. A 37 pp 2243– (1988)
[53] Holmes, P. J., Physica D 21 pp 7– (1986) · Zbl 0623.58014
[54] Holmes, P. J., Arch. Ration. Mech. Anal. 90 pp 115– (1985) · Zbl 0593.58027
[55] Hong, F. L., J. Opt. Soc. Am. B 6 pp 1378– (1989)
[56] King, G. P., Phys. Rev. A 46 pp 3092– (1992)
[57] Klinker, T., Phys. Lett. A 101 pp 371– (1984)
[58] Knop, W., J. Chem. Phys. 93 pp 3950– (1990)
[59] Kocarev, L., Phys. Lett. A 190 pp 399– (1994) · Zbl 0960.37501
[60] Kurz, T., Phys. Rev. A 37 pp 1029– (1987)
[61] Lathrop, D. P., Phys. Rev. A 40 pp 4028– (1989)
[62] Lauterborn, W., J. Opt. Soc. Am. B 5 pp 1097– (1988)
[63] Lawandy, N. M., IEEE J. Quantum Electron. 16 pp 701– (1980)
[64] Lefebvre, M., Phys. Rev. A 29 pp 758– (1984)
[65] Lefranc, M., Int. J. Bifurcation Chaos Appl. Sci. Eng. 3 pp 643– (1993) · Zbl 0875.78007
[66] Lefranc, M., J. Opt. Soc. Am. B 8 pp 239– (1991)
[67] Letellier, C., Phys. Rev. E 52 pp 4754– (1995)
[68] Lorenz, E. N., J. Atmos. Sci. 20 pp 130– (1963) · Zbl 1417.37129
[69] Lorenz, E. N., Ann. (N.Y.) Acad. Sci. 357 pp 282– (1980)
[70] Los, J., Proc. London Math. Soc. 66 pp 1– (1993)
[71] Mancho, A. M., Phys. Lett. A 221 pp 181– (1996) · Zbl 1098.37507
[72] Matorin, I. I., Sov. J. Quantum Electron. 14 pp 1401– (1984)
[73] Melvin, P., Phys. Rev. A 44 pp 3419– (1991)
[74] Metropolis, M., J. Comb. Theory, Ser. A 15 pp 25– (1973) · Zbl 0259.26003
[75] Midavaine, T., Phys. Rev. Lett. 55 pp 1989– (1986)
[76] Mindlin, G. B., Physica D 58 pp 229– (1992) · Zbl 1194.37135
[77] Mindlin, G. B., Phys. Rev. Lett. 64 pp 2350– (1990) · Zbl 1050.37509
[78] Mindlin, G. B., Phys. Rev. E 48 pp 4297– (1993)
[79] Mindlin, G. B., Phys. Rev. E 54 pp 1497– (1995)
[80] Mindlin, G. B., J. Nonlinear Sci. 1 pp 147– (1991) · Zbl 0797.58057
[81] Newhouse, S. E., Topology 13 pp 9– (1974) · Zbl 0275.58016
[82] Oseledec, V. I., Trans. Mosc. Math. Soc. 19 pp 197– (1968)
[83] Packard, N. H., Phys. Rev. Lett. 45 pp 712– (1980)
[84] Papoff, F., Phys. Rev. Lett. 68 pp 1128– (1992)
[85] Parlitz, U., J. Acoust. Soc. Am. 88 pp 1061– (1990)
[86] Parlitz, U., Phys. Lett. 107A pp 351– (1985)
[87] Pecora, L. M., Phys. Rev. Lett. 64 pp 821– (1990) · Zbl 0938.37019
[88] Puccioni, G. P., Phys. Rev. Lett. 55 pp 339– (1985)
[89] Richetti, P., J. Stat. Phys. 48 pp 977– (1987) · Zbl 0925.58052
[90] Roldán, E., Quantum Semiclassic. Opt. 9 pp R1– (1997)
[91] Roux, J.-C., Physica D 8 pp 257– (1983) · Zbl 0538.58024
[92] Rössler, O. E., Phys. Lett. A 57 pp 397– (1976) · Zbl 1371.37062
[93] Rössler, O. E., Z. Naturforsch. A 31a pp 1664– (1976)
[94] Satija, I. I., Phys. Lett. A 112 pp 183– (1985)
[95] Sauer, T., Physica A 58 pp 193– (1992)
[96] Sauer, T., J. Stat. Phys. 65 pp 579– (1991) · Zbl 0943.37506
[97] Scheffczyk, C., Phys. Rev. A 43 pp 6495– (1991)
[98] Schwartz, I. B., J. Math. Biol. 18 pp 233– (1983) · Zbl 0523.92020
[99] Shaw, R., Z. Naturforsch. A 36a pp 80– (1981)
[100] Shil’nikov, A. L., Physica D 62 pp 338– (1993) · Zbl 0783.58052
[101] Shimizu, T., Phys. Lett. A 76 pp 201– (1980)
[102] Shinriki, M., Proc. IEEE 69 pp 394– (1981)
[103] Šilnikov, L. P., Sov. Math. Dokl. 66 pp 163– (1965)
[104] Singer, J., Phys. Rev. Lett. 66 pp 1123– (1991)
[105] Smale, S., Bull. Am. Math. Soc. 73 pp 747– (1967) · Zbl 0202.55202
[106] Solari, H. G., Opt. Commun. 64 pp 49– (1987)
[107] Solari, H. G., Phys. Rev. A 37 pp 3096– (1988)
[108] Solari, H. G., Phys. Rev. E 54 pp 3185– (1996)
[109] Tredicce, J. R., Opt. Commun. 55 pp 131– (1985)
[110] Tredicce, J. R., J. Opt. Soc. Am. B 2 pp 173– (1985)
[111] Tredicce, J. R., Phys. Rev. A 34 pp 2073– (1986)
[112] Tufillaro, N. B., Phys. Rev. E 50 pp 4509– (1994)
[113] Tufillaro, N. B., Phys. Rev. A 44 pp 4786– (1991)
[114] Tufillaro, N. B., Phys. Rev. A 41 pp 5717– (1990)
[115] Tufillaro, N. B., Phys. Rev. E 51 pp 164– (1995)
[116] Uezu, T., Phys. Lett. A 93 pp 161– (1983)
[117] Uezu, T., Prog. Theor. Phys. 68 pp 1907– (1982) · Zbl 1069.37513
[118] van Buskirk, R., Phys. Rev. A 31 pp 3332– (1985)
[119] van der Pol, B., Philos. Mag. 3 pp 65– (1927)
[120] Waldner, F., J. Magn. Magn. Mater. 54–57 pp 1135– (1986)
[121] Wedding, B., Phys. Lett. A 105 pp 105– (1984)
[122] Weiss, C. O., J. Opt. Soc. Am. B 2 pp 137– (1985)
[123] Weiss, C. O., Phys. Rev. Lett. 50 pp 413– (1986)
[124] Weiss, C. O., Opt. Commun. 57 pp 2804– (1984)
[125] Whitney, H., Ann. Math. 37 pp 645– (1936) · Zbl 0015.32001
[126] Wolf, A., Physica D 16 pp 285– (1985) · Zbl 0585.58037
[127] Zambon, B., Phys. Rev. A 44 pp R688– (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.