×
Arneodo, A.; Coullet, Pierre; Tresser, Charles

Possible new strange attractors with spiral structure. (English) Zbl 0485.58013

Commun. Math. Phys. 79, 573-579 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0485.58013

Cited in 4 Reviews
Cited in 123 Documents

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37G99 Local and nonlocal bifurcation theory for dynamical systems
34C25 Periodic solutions to ordinary differential equations

Keywords:

strange attractors; homoclinic solution; denumerable set of unstable periodic solutions of saddle type; attractor of spiral structure; differential equation in 3-space

Citations:

Zbl 0136.082
Cite Review PDF
Full Text: DOI

References:

[1] Gurel, O., Rössler, O.E.: Ann. N.Y. Acad. Sci.316 (1979)
[2] Smale, S.: Bull. Am. Math. Soc.73, 747 (1967) · Zbl 0202.55202 · doi:10.1090/S0002-9904-1967-11798-1
[3] Bowen, R., Ruelle, D.: Invent. math.29, 181 (1975) · Zbl 0311.58010 · doi:10.1007/BF01389848
[4] Henon, M.: Commun. Math. Phys.50, 69 (1976) · Zbl 0576.58018 · doi:10.1007/BF01608556
[5] Curry, J.H., Yorke, J.A.: The structure of Attractors in dyn. systems. Markley et al. (ed). In: Lecture notes in mathematics. Vol. 668, 48, Berlin, Heidelberg, New York: Springer 1978
[6] Rössler, O.E.: Phys. Lett.57A, 397 (1976)
[7] Devaney, R., Nitecki, Z.: Commun. Math. Phys.67, 137 (1979) · Zbl 0414.58028 · doi:10.1007/BF01221362
[8] Marotto, F.R.: Commun. Math. Phys.68, 187 (1979) · Zbl 0414.58023 · doi:10.1007/BF01418128
[9] Misiurewicz, M., Szewc, B.: Warszawa Preprint (1979)
[10] Tresser, C., Coullet, P., Arneodo, A.: J. Phys. A13, L-123 (1980)
[11] Newhouse, S.: Publ. I.H.E.S.50, 101 (1979)
[12] Newhouse, S., Palis, J.: Dynamical systems. Peixoto, M. (ed.). New York: Academic Press 1973
[13] Misiurewicz, M.: Talk given at the International Conference on Nonlinear Dynamics held at New-York on December 1979
[14] Lorenz, E.N.: J. Atmos. Sci.20, 130 (1963) · Zbl 1417.37129 · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[15] Guckenheimer, J.: Hopf bifurcation and its applications. Marsden, J.E., Mc Craken, M. (eds.). In: Applied Mathematical Science, Vol. 19. New York: Springer 1976
[16] Guckenheimer, J., Williams, R.F.: Publ. I.H.E.S.50, 59 (1979)
[17] Williams, R.F.: Publ. I.H.E.S.50, 73 (1979)
[18] Coullet, P., Tresser, C., Arneodo, A.: Phys. Lett.72A, 268 (1979)
[19] Shil’nikov, L.P.: Sov. Mat. Dok.6, 163 (1965)
[20] Shil’nikov, L.P.: Mat. USSR. Sb.10, 91 (1970) · Zbl 0216.11201 · doi:10.1070/SM1970v010n01ABEH001588
[21] Hartman, P.: Ordinary differential equations. New-York: Wiley 1964 · Zbl 0125.32102
[22] Grobman, D.: Dokl. Akad. Nauk. USSR128, 880 (1965)
[23] Sternberg, S.: Am. J. Math.80, 623 (1958) · Zbl 0083.31406 · doi:10.2307/2372774
[24] Arneodo, A., Coullet, P., Tresser, C.: Nice Preprint NTH 80/7
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.