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manifold; foliation; duffing oscillator

References:

[1] Anosov, D. V.: **Foliation. Encyclopedia of Mathematics**. Michiel Hazewinkel Kluwer Academic Publishers (2001). MR 1935796

[2] Moerdijk, I., Mrcun, J.: **Introduction to foliations and Lie groupoids**. Cambridge Studies in Advanced Mathematics 91 (2003), 318-320. MR 2012261 | Zbl 1029.58012

[3] Packard, N. H., Crutchfield, J. P., Farmer, J. D., Shaw, R. S.: **Geometry from a Time Series**. Physical Review Letter 45 (1980), 712-715. DOI 10.1103/PhysRevLett.45.712

[4] Takens, F.: **Detecting Strange Attractors in Turbulence**. Lecture Notes in Mathematics 898 D. A. Rand and L. S. Young (1981), 366-381. DOI 10.1007/BFb0091924 | MR 0654900 | Zbl 0513.58032

[5] Vaidya, P. G., Majumder, S.: **Embedding in higher dimension causes ambiguity for the problem of determining equation from data**. European Physics Journal, special topic 165 (2008), 15-24. DOI 10.1140/epjst/e2008-00845-1

[6] Vaidya, P. G., Angadi, S.: **A Computational Procedure to Generate a Difference Equations from Differential Equation**. New Progress in Difference Equations Proceedings of the 6th ICDEA in Augsburg (2003), 539-548.

[7] Guckenheimer, J., Holmes, P.: **Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields**. Springer, New York (1983). MR 0709768 | Zbl 0515.34001

[8] Sepulchre, J. A., MacKay, R. S.: **Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators**. Nonlinearity 10 (1997), 679-713. DOI 10.1088/0951-7715/10/3/006 | MR 1448582 | Zbl 0905.39004

[9] Pokorny, P.: **Continuation of Periodic Solutions of Dissipative and Conservative Systems: Application to Elastic Pendulum**. Math. Probl. Eng. 2009, Article ID 104547, p. 15, doi: 10.1155/2009/104547. MR 2530049