Abstract
An empirical method that uses colors and rotation of 3D figures is proposed for visualizing the 4D “Poincaré space of section” in 3D Hamiltonian systems. The representation of the 4th dimension as color variation in 3D projections, gives essential information about the areas that are close to each other in the 4D space. This method helps us to reveal existing structures in cases where the consequents in the 3D projections seem to fill densely the space.
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References
Contopoulos G., Magnenat P. and Martinet L.: 1982, Physica D, Vol.6D 123.
Contopoulos G.: 1984, in “Nonlinear Phenomena in Physics” (ed.F. Claro), p.238, Springer Verlag.
Contopoulos G. and Magnenat P.: 1985, Celest. Mech. 37, 387.
May A. and Binney J.: 1986, MNRAS 221, 857.
Magnenat P.: 1982, Cel. Mech. 28, 319.
Martinet L. & Magnenat P.: 1981, Astron. & Astroph. 96, 68.
Patsis P.A. & Zachilas L.: 1990, Astron. & Astroph. 227, 37.
Patsis P.A. & Zachilas L.: 1994, “Using colors and rotation for visualizing 4-dimensional Poincare Cross Sections”, to appear in Int. J. Bifurcation and Chaos.
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© 1994 Springer Science+Business Media New York
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Patsis, P.A., Zachilas, L. (1994). A method for Visualizing the 4-Dimensional Space of Section in 3-D Hamiltonian Systems. In: Seimenis, J. (eds) Hamiltonian Mechanics. NATO ASI Series, vol 331. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0964-0_43
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DOI: https://doi.org/10.1007/978-1-4899-0964-0_43
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