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Communications in Mathematical Physics

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

Characteristic exponents and strange attractors

  • Sidnie Dresher Feit
Article

Abstract

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.

Keywords

Neural Network Statistical Physic Complex System Asymptotic Behavior Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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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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