TY - JOUR
T1 - Chaos and crises in more than two dimensions
AU - Moresco, Pablo
AU - Dawson, Silvina Ponce
PY - 1997
Y1 - 1997
N2 - Noisy chaotic trajectories, with finite-time Lyapunov exponents that fluctuate about zero, are basically unshadowable [S. Dawson, C. Grebogi, T. Sauer, and J. A. Yorke, Phys. Rev. Lett 73, 1927 (1994)]. This can occur when periodic orbits, with different numbers of unstable directions, coexist inside the attractor. The presence of a Hénon-type chaotic saddle (i.e., a nonattracting chaotic set with a structure similar to that of the Hénon attractor) guarantees such coexistence in a persistent manner [S. P. Dawson, Phys. Rev. Lett. 76, 4348 (1996)]. In this paper, we describe how these sets appear naturally in maps of more than two dimensions, how they can be found, and what crises they produce.
AB - Noisy chaotic trajectories, with finite-time Lyapunov exponents that fluctuate about zero, are basically unshadowable [S. Dawson, C. Grebogi, T. Sauer, and J. A. Yorke, Phys. Rev. Lett 73, 1927 (1994)]. This can occur when periodic orbits, with different numbers of unstable directions, coexist inside the attractor. The presence of a Hénon-type chaotic saddle (i.e., a nonattracting chaotic set with a structure similar to that of the Hénon attractor) guarantees such coexistence in a persistent manner [S. P. Dawson, Phys. Rev. Lett. 76, 4348 (1996)]. In this paper, we describe how these sets appear naturally in maps of more than two dimensions, how they can be found, and what crises they produce.
UR - https://www.scopus.com/pages/publications/0008025028
U2 - 10.1103/PhysRevE.55.5350
DO - 10.1103/PhysRevE.55.5350
M3 - Article
AN - SCOPUS:0008025028
SN - 1063-651X
VL - 55
SP - 5350
EP - 5360
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 5
ER -