In this note,we mainly prove that the following conclusion is true not only for a circte map with a periodic point but also for a general circle map f. It is R(f) Λ(R(f) ) Λ(Λ(f)) Λ(Ω(f)) R(f) ) Λ(f) Ω(f) .
In the theory of the universal phenomenon obtained in the numerical research aboutinterval maps and circle maps,a key role is played by the renormalization group hinctionalequations and their solutions.
A new theoretical model for low dimenSional dynandrs of the heart employing two-parameter circle maps is used to study the nature of the transition from regular periodic dynalines to ocular, chaotic dynandes.
This paper has shown that the two -dimensional bifurcation structure and scaling properties of able maps in human heart can be largely detendned using numerical methods based upon calculation of the Lyapunov exponent specturm.
We prove the existence of fixed points of p-tupling renormalization operators for interval and circle mappings having a critical point of arbitrary real degree r >amp;gt; 1.