next up previous
Next: Figures Up: Table of Contents Previous: Conclusion


Berry, M.V. [1981] ``Regularity and chaos in classical mechanics, illustrated by three deformations of a circle 'billiard','' Eur. J. Phys. 2, 91-102.

Birkhoff, G.D. [1927] ``On the periodic motion of dynamical systems,'' Acta Mathematica 50, 359-379.

Bleher, S., Grebogi, C., Ott, E. & Brown, R. [1988] ``Fractal boundaries for exit in Hamiltonian dynamics,'' Phys. Rev. A 38, 930-938 - Abstract.

Bleher, S., Grebogi, C. & Ott, E. [1990] ``Bifurcation to chaotic scattering,'' Physica D 46, 87-121.

Boyd, P.T. & McMillan, S.L.W. [1992] ``Initial-value space structure in irregular gravitational scattering,'' Phys. Rev. A 46, 6277-6287.

Chen, J., Rexford, J.L. & Lee, Y.C. [1990] ``Fractal boundaries in magnetotail particle dynamics,'' Geophys. Res. Lett. 17, 1049-1052.

Chen, J., [1992] ``Nonlinear dynamics of charged particles in the magnetotail,'' J. Geophys. Res. 97, 15011-15050.

Ding, M., Grebogi, C., Ott, E. & Yorke, J.A. [1990] ``Transition to chaotic scattering,'' Phys. Rev. A 42, 7025-7040 - Abstract.

Eckhardt, B. [1987] ``Fractal properties of scattering singularities,'' J. Phys. A 20, 5971-5979.

Eckhardt, B. [1988] ``Irregular scattering,'' Physica D 33, 89-98.

Gaspard, P. & Ramirez, D.A. [1992] ``Ruelle classical resonances and dynamical chaos: the three- and four-disk scatterers,'' Phys. Rev. A 45, 8383-8397.

Gaspard, P. & Rice, S.A. [1989a] ``Scattering from a classically chaotic repellor,'' J. Chem. Phys. 90, 2225-2241.

Gaspard, P. & Rice, S.A. [1989b] ``Semiclassical quantization of the scattering from a classically chaotic repellor,'' J. Chem. Phys. 90, 2242-2254.

Gaspard, P. & Rice, S.A. [1989c] ``Exact quantization of the scattering from a classically chaotic repellor,'' J. Chem. Phys. 90, 2255-2262.

Grebogi, C., Ott, E. & Yorke, J.A. [1983a] ``Fractal basin boundaries, long-lived chaotic transients, and unstable-unstable pair bifurcation,'' Phys. Rev. Lett. 50, 935-938.

Grebogi, C., McDonald, S.W., Ott, E. & Yorke, J.A. [1983b] ``Final state sensitivity: an obstruction to predictability,'' Phys. Lett. A 99, 415.

Grebogi, C., Ott, E. & Yorke, J.A. [1986] ``Metamorphoses of basin boundaries in nonlinear dynamical systems,'' Phys. Rev. Lett. 56, 1011-1014.

Grebogi, C., Ott, E., Varosi, F. & Yorke, J.A. [1987a] Cover of IEEE Spectrum, April.

Grebogi, C., Kostelich, E., Ott, E. & Yorke, J.A. [1987b] ``Multi-dimensioned intertwined basin boundaries: basin structure of the kicked double rotor,'' Physica D 25, 347-360.

Grebogi, E., Ott, E. & Yorke, J.A. [1987c] ``Basin boundary metamorphoses: changes in accessible boundary orbits,'' Physica D 24, 243-262 - Abstract.

Grebogi, E., Nusse, H.E., Ott, E. & Yorke, J.A. [1988] ``Basic sets: sets that determine the dimension of basin boundaries,'' in Lecture Notes in Mathematics, Vol. 1342, ed. J.C. Alexander (Springer-Verlag, New York) pp. 220-250.

Gwinn, E.G. & Westervelt, R.M. [1986] ``Fractal basin boundaries and intermittency in the driven damped pendulum,'' Phys. Rev. A 33, 4143-4155.

Hénon, M. [1988] ``Chaotic scattering modeled by an inclined billiard,'' Physica D 33, 132-156.

Hsu, G.-H., Ott, E., & Grebogi, C. [1988] ``Strange saddles and the dimensions of their invariant manifolds,'' Phys. Lett. A, 127, 199-204.

Jalabert, R.A., Baranger, H.U., & Stone, A.D. [1990] ``Conductance fluctuations in the ballistic regime: a probe of quantum chaos?,'' Phys. Rev. Lett. 65, 2442

Jung, C. [1986] ``Poincaré map for scattering system,'' J. Phys. A 19, 1345-1353.

Kantz, K. & Grassberger P. [1985] ``Repellers, semi-attractors, and long-lived chaotic transients,'' Physica D 17, 75-86.

Kennedy, J. & Yorke, J.A. [1991] ``Basins of Wada,'' Physica D 51, 213-225 - Abstract.

Kovács, Z. & Tél, T. [1990] ``Thermodynamics of irregular scattering,'' Phys. Rev. Lett. 64, 1617-1620.

Lai, Y.-C., Grebogi, C., Blümel, R. & Kan, I. [1993] ``Crises in chaotic scattering,'' Phys. Rev. Lett. 71, 2212-2215 - Abstract.

McDonald, S.W., Grebogi, C., Ott, E. & Yorke, J.A. [1985] ``Fractal basin boundaries,'' Physica D 17, 125-153 - Abstract.

Moon, F.C. & Li, G.-X. [1985] ``Fractal basin boundaries and homoclinic orbits for periodic motions in a two-well potential,'' Phys. Rev. Lett. 55, 1439-1442.

Noid, D.W., Gray, S. & Rice, S.A. [1986], ``Fractal behavior in classical collisional energy transfer,'' J. Chem. Phys. 84, 2649-2652.

Nusse, H.E., Ott, E. & Yorke, J.A. [1995] ``Saddle-node bifurcations on fractal basin boundaries,'' Phys. Rev. Lett 75, 2482-2485.

Nusse, H.E. & Yorke, J.A. [1995] ``Wada basin boundaries and basin cells,'' Physica D (to appear).

Ott, E. [1993] Chaos in Dynamical Systems (Cambridge University Press, New York), Chap. 5, pp. 151-183.

Ott, E. & Tél, T. [1993] ``Chaotic scattering: An introduction,'' Chaos 3, 417-426 and references therein - Abstract.

Smilansky, U. [1992] ``The classical and quantum theory of chaotic scattering,'' in Chaos and Quantum Physics, eds. Giannoni, M.-J., Voros, A., & Zinn-Justin, J. (Elsevier, Amsterdam).

Takesue, S. & Kaneko, K. [1984] ``Fractal basin structure'' Progr. Theor. Phys. 71, 35-49.

Troll, G. [1991] ``A devil's staircase in chaotic scattering,'' Physica D 50, 276-296.

Yoneyama, K. [1917] ``Theory of continuous sets of points,'' Tohoku Math. J. 11-12, 43.

You, Z., Kostelich, E.J. & Yorke, J.A. [1991] ``Calculating stable and unstable manifolds,'' Int. J. Bifurcation and Chaos, 1, 605-623 - Abstract.

next up previous
Next: Figures Up: Table of Contents Previous: Conclusion

Chaos at Maryland Home Page