Connecting curves for dynamical systems

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 25, 2010, Pages

  Gilmore, R ^a   Ginoux, Jean Marc ^b   Jones, Timothy ^a   Letellier, C ^c   Freitas, U S ^c  

^a DREXEL UNIVERSITY   (United States)

^b INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

^c UNIVERSITÉ DE ROUEN   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77953003427     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/25/255101     Document Type: Article

References (20)

1. Poincaré H 1881 Sur les courbes définies par une équation differentielle J. Math. Pures Appl. III 7 375-422
2. Poincaré H 1882 Sur les courbes définies par une équation différentielle J. Math Pures Appl. III 8 251-96
3. Poincaré H 1885 Sur les courbes définies par une équation différentielle J. Math. Pures Appl. IV 1 167-244
4. Poincaré H 1886 Sur les courbes définies par une équation differentielle J. Math. Pures Appl. IV 2 151-217
5. Roth M and Peikert R 1998 A higher-order method for finding vortex core lines Proc. IEEE Conf. on Visualization'98 pp 143-50
6. Coddington E A and Levinson N 1995 Theory of Ordinary Differential Equations (New York: McGraw-Hill)
7. Frechet M 1925 La notion de differentielle dans l'analyse generale Ann. Sci. l'Ecole Normale Superieure, Ser. 3 42 293-323
8. Ginoux J M 2009 Differential Geometry Applied to Dynamical Systems (World Scientific Series on Nonlinear Science, Series A vol 66) (Singapore: World Scientific)
9. Ginoux J M and Rossetto R 2006 Slow manifold of a neuronal bursting model Understanding Complex Systems (Heidelberg: Springer)
10. Ginoux J M, Rossetto B and Chua L O 2008 Slow invariant manifolds as curvature of the flow of dynamical systems Int. J. Bifurcation Chaos 18 3409-30
11. Struik D J 1961 Lectures on Classical Differential Geometry (New York: Dover)
12. Kreyszig E 1959 Differential Geometry (New York: Dover)
13. Gray A, Salamon S and Abbena E 2006 Modern Differential Geometry of Curves and Surfaces with Mathematica (London: Chapman and Hall/CRC)
14. Wilkinson S 1999 Intersection of surfaces Math. Educ. Res. 8 5-10
15. Rössler O E 1976 An equation for continuous chaos Phys. Lett. A 57 397-8
16. Lorenz E N 1963 Deterministic nonperiodic flow J. Atmos. Sci. 20 130-41
17. Byrne G, Gilmore R and Letellier C 2004 Distinguishing between folding and tearing mechanisms in strange attractors Phys. Rev. E 70 056214
18. Lorenz E N 1984 Irregularity: a fundamental property of the atmosphere Tellus 36A 98-110
19. Rössler O E 1979 An equation for hyperchaos Phys. Lett. A 71 155-7
20. Thomas R 1999 Deterministic chaos seen in terms of feedback circuits: analysis, synthesis, 'labyrinth chaos' Int. J. Bifurcation Chaos 9 1889-905