Complutense University Library

On scattering trajectories of dynamical systems.

Díaz-Cano Ocaña, Antonio and Gonzalez Gascón, F. and Peralta Salas, Daniel (2006) On scattering trajectories of dynamical systems. Journal of Mathematical Physics, 47 (6). 062703-1. ISSN 0022-2488

[img] PDF
Restricted to Repository staff only

738kB

Official URL: http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000047000006062703000001&idtype=cvips&doi=10.1063/1.2206880&prog=normal

View download statistics for this eprint

==>>> Export to other formats

Abstract

Dynamical systems on R-n presenting geometric chaos, i.e., open domains where bounded and unbounded orbits are intermingled, have been constructed. The opposite situation (open scattering) has been studied for integrable Hamiltonian and non-Hamiltonian vector fields and for equations of type x=-del V(x) when the potential has the form V=a(r)+b(r)F(theta) in spherical coordinates.

Item Type:Article
Subjects:Sciences > Physics > Mathematical physics
ID Code:15022
References:

V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer, New York, 1978).

F. González-Gascón, Nuovo Cimento Soc. Ital. Fis., B 111, 1247 1996.

S. Bleher, C. Grebogi, and E. Ott, Physica D 46, 87 1990.

M. Ding, C. Grebogi, E. Ott, and J. Yorke, Phys. Rev. A 42, 7025 1990.

L. Poon, J. Campos, E. Ott, and C. Grebogi, Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, 251 1996.

L. Benet, C. Jung, T. Papenbrock, and T. H. Seligman, Physica D 131, 254 1999.

J. Aguirre, J. C. Vallejo, and M. A. F. Sanjuán, Phys. Rev. E 64, 066208 2001.

J. Seoane, J. Aguirre, M. A. F. Sanjuán, and Y. C. Lai, Chaos in press.

A. F. Costa, F. González-Gascón, and A. González-López, Invent. Math. 93, 545 1988.

V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics Springer,Berlin, 1997.

V. I. Arnold, Dokl. Akad. Nauk SSSR 156, 9 1964.

B. Chirikov, Phys. Rep. 52, 264 1979.

F. González-Gascón and D. Peralta-Salas, Phys. Lett. A 333, 72 2004.

J. Stallings, Proc. Cambridge Philos. Soc. 58, 481 1962.

M. Gromov, Invent. Math. 82, 307 1985.

L. Bates and G. Peschke, J. Diff. Geom. 32, 533 1990.

J. Hale and H. Koçak, Dynamics and Bifurcations Springer, New York, 1991.

J. Kotus, Proc. Am. Math. Soc. 108, 1039 1990.

D. D’Acunto, C. R. Acad. Sci. Paris Ser. I 337, 327 2003.

R. Abraham and J. Robbin, Transversal Mappings and Flows Benjamin, New York, 1967.

L. A. Pars, A Treatise on Analytical Dynamics Heinemann, London, 1965.

F. González-Gascón and D. Peralta-Salas, J. Phys. A 33, 5361 2000.

F. González-Gascón and D. Peralta-Salas, J. Phys. A 36, 6441 2003.

Deposited On:26 Apr 2012 08:25
Last Modified:06 Feb 2014 10:14

Repository Staff Only: item control page