Communications in Mathematical Physics

, Volume 61, Issue 3, pp 249–260 | Cite as

Characteristic exponents and strange attractors

  • Sidnie Dresher Feit


Iterates of maps in the familyf(x,y)=(y+1−Ax2,Bx) (see [1]) are investigated. Characteristic exponents\(C_p = \mathop {\lim }\limits_{n \to \infty } (1/n)\log \left\| {df^n (p)} \right\|\) are estimated numerically. Further numerical investigations indicate that finiteC p >0 corresponds to a strange attractor. WhenC values are calculated forB fixed andA in an interval, one finds dispersed amongC>0 values many small subintervals for which 0>C. On each such subinterval there appear to be attractors of periodk, 2k, 4k, ... the period doubling asA increases. Many different values ofk have been observed. A theorem is proved forA>0, 1>B > 0 describing an explicit compact setK (depending onA andB) such that all non-divergent asymptotic behavior takes place inK.


Neural Network Statistical Physic Complex System Asymptotic Behavior Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Sidnie Dresher Feit
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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