×

Topological horseshoes and computer assisted verification of chaotic dynamics. (English) Zbl 1168.37301


MSC:

37B10 Symbolic dynamics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37B40 Topological entropy
37N99 Applications of dynamical systems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.1070/SM1968v005n01ABEH002587 · Zbl 0198.56903
[2] DOI: 10.1070/SM1968v006n04ABEH001074 · Zbl 0198.57001
[3] DOI: 10.1070/SM1969v007n01ABEH001076 · Zbl 0198.57002
[4] Birkhoff G. D., Amer. Math. Soc. Colloq. Publication 9 (1927)
[5] Birkhoff G. D., Mém. Pont. Acad. Sci. Novi Lyncaei 1 pp 85–
[6] DOI: 10.1007/BF02104512 · Zbl 0945.37003
[7] DOI: 10.1017/S0143385700000171 · Zbl 0971.37005
[8] DOI: 10.1017/CBO9780511754494
[9] DOI: 10.1016/0022-0396(75)90037-6 · Zbl 0293.58011
[10] DOI: 10.1016/0022-0396(78)90123-7 · Zbl 0392.58003
[11] DOI: 10.1142/S0218127497000224 · Zbl 0886.58078
[12] DOI: 10.1016/S0167-2789(97)00233-9 · Zbl 0941.37018
[13] DOI: 10.1137/S1111111101394040 · Zbl 1002.92005
[14] Hadamard J., J. Math. Pures. Appl. 4 pp 27–
[15] Hadamard J., Bull. Soc. Math. France pp 224–
[16] DOI: 10.1007/s10910-005-4537-2 · Zbl 1217.37028
[17] DOI: 10.1007/s10910-005-9043-z · Zbl 1096.92059
[18] DOI: 10.2307/2695795 · Zbl 0991.37015
[19] DOI: 10.1090/S0002-9947-01-02586-7 · Zbl 0972.37011
[20] DOI: 10.2307/1969357
[21] DOI: 10.1088/0305-4470/39/29/009 · Zbl 1097.37026
[22] DOI: 10.1002/cta.400 · Zbl 1191.94146
[23] DOI: 10.1090/S0273-0979-1995-00558-6 · Zbl 0820.58042
[24] DOI: 10.2307/2371264 · Zbl 0019.33502
[25] Pireddu M., Adv. Nonlin. Stud. 5 pp 411–
[26] Poincaré H., Les Méthodes Nouvelles de la Mécanique Céleste 3 (1899)
[27] DOI: 10.1017/CBO9780511752537
[28] Robinson C., Dynamical Systems: Stability, Symbolic Dynamics, and Chaos (1995) · Zbl 0853.58001
[29] DOI: 10.1090/S0002-9904-1967-11798-1 · Zbl 0202.55202
[30] Smale S., Essays on Dynamical Systems, Economic Process, and Related Topics (1980) · Zbl 0451.58001
[31] DOI: 10.1007/BF03024399 · Zbl 0983.37001
[32] DOI: 10.1006/jdeq.1996.3222 · Zbl 0873.58049
[33] DOI: 10.1016/0040-9383(95)00029-1 · Zbl 0855.58023
[34] DOI: 10.1007/978-1-4612-1042-9
[35] Yang X.-S., Chaos Solit. Fract. 20 pp 149–
[36] DOI: 10.1016/S0960-0779(03)00202-9 · Zbl 1053.37006
[37] DOI: 10.1142/S0218127404010060 · Zbl 1129.37361
[38] DOI: 10.1142/S0218127405011631
[39] DOI: 10.1088/0305-4470/38/19/008 · Zbl 1073.37040
[40] DOI: 10.1063/1.2220476 · Zbl 1146.37371
[41] DOI: 10.1142/S0218127406014666 · Zbl 1093.92009
[42] DOI: 10.1016/j.chaos.2005.04.017 · Zbl 1083.37034
[43] DOI: 10.1142/S0218127407018968
[44] DOI: 10.1016/j.apm.2007.06.008 · Zbl 1179.37035
[45] DOI: 10.1142/S0218127407020026 · Zbl 1298.92025
[46] DOI: 10.1142/S0218127408021762 · Zbl 1165.34356
[47] DOI: 10.1088/0951-7715/10/1/016 · Zbl 0907.58048
[48] DOI: 10.1016/j.jde.2004.03.013 · Zbl 1061.37013
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.