×

Differential geometry and mechanics: applications to chaotic dynamical systems. (English) Zbl 1111.37021


MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C10 Dynamics induced by flows and semiflows
53A04 Curves in Euclidean and related spaces
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics

Software:

CandS
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] Andronov A. A., Theory of Oscillators (1966)
[2] DOI: 10.1016/j.physd.2004.10.006 · Zbl 1063.37023
[3] DOI: 10.1109/TCS.1986.1085869 · Zbl 0634.58015
[4] Coddington E. A., Theory of Ordinary Differential Equations (1955) · Zbl 0064.33002
[5] Delachet A., ”Que sais-je”, n{\(\deg\)}1104, in: La Géométrie Différentielle (1964)
[6] Gause G. F., The Struggle for Existence (1935)
[7] Ginoux J. M., Int. J. Bifurcation and Chaos 5 pp 1689–
[8] Gray A., Modern Differential Geometry of Curves and Surfaces with Mathematica (2006) · Zbl 1123.53001
[9] Kaplan J., Lecture Notes in Mathematics 730 pp 204– (1979)
[10] Kreyszig E., Differential Geometry (1991)
[11] DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 · Zbl 1417.37129
[12] Poincaré H., J. Math. Pures et Appl. 7 pp 375–
[13] Poincaré H., J. Math. Pures et Appl. 8 pp 251–
[14] Poincaré H., J. Math. Pures et Appl. 1 pp 167–
[15] Poincaré H., J. Math. Pures et Appl. 2 pp 151–
[16] Rossetto B., Lecture Notes in Physics 278 pp 12– (1986)
[17] DOI: 10.1142/S0218127498001765 · Zbl 0941.37010
[18] Struik D. J., Lecture on Classical Differential Geometry (1988) · Zbl 0697.53002
[19] Tihonov A. N., Mat. Sbornik N.S. 31 pp 575–
[20] Van der Pol B., Phil. Mag. 7 pp 978–
[21] Verhulst P. F., Corresp. Math. Phys. pp 113–
[22] Volterra V., Mem. Acad. Lincei III 6 pp 31–
[23] Volterra V., Leçons sur la Théorie Mathématique de la Lutte pour la Vie (1931)
[24] DOI: 10.1016/0167-2789(85)90011-9 · Zbl 0585.58037
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.