Electronic Resource
Woodbury, NY
:
American Institute of Physics (AIP)
Chaos
6 (1996), S. 108-120
ISSN:
1089-7682
Source:
AIP Digital Archive
Topics:
Physics
Notes:
In this paper we are concerned with the dynamics of noninvertible transformations of the plane. Three examples are explored and possibly a new bifurcation, or "eruption,'' is described. A fundamental role is played by the interactions of fixed points and singular curves. Other critical elements in the phase space include periodic points and an invariant line. The dynamics along the invariant line, in two of the examples, reduces to the one-dimensional Newton's method which is conjugate to a degree two rational map. We also determine, computationally, the characteristic exponents for all of the systems. An unexpected coincidence is that the parameter range where the invariant line becomes neutrally stable, as measured by a zero Lyapunov exponent, coincides with the merging of a periodic point with a point on a singular curve. © 1996 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.166158
Permalink
| Library |
Location |
Call Number |
Volume/Issue/Year |
Availability |
