KS entropy of measure-preserving mappings with parabolic fixed point

Details KS entropy of measure-preserving mappings with parabolic fixed point KS entropy of measure-preserving mappings with parabolic fixed point

Jul 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cha%26a..18..340z&link_type=abstract

Chinese Astronomy and Astrophysics, Volume 18, Issue 3, p. 340-348.

Astronomy and Astrophysics

Astrophysics

Ks Entropy, Measure-Preserving Mapping, Parabolic Invariant Point

Scientific paper

In this paper we consider the variation of the KS entropy with the parameters A, B, C, D, E in the 2-dimensional measure-preserving mapping with a parabolic fixed point, T2:{xn+1=xn-Ayn3yn+1=xn+yn-Ay3n and its perturbed extension, T3:{xn+1=xn-Ayn3+Bsinznyn+1=xn+yn-Ay3n+Csinxn+1zn+1=zn+Dsinyn+1+E(mod2π)
Numerical exploration shows that the KS entropy of T2 within a certain defined region of the phase space is independent of A, as expected from theory. For T3, the KS entropy increases with B, C, D and decreases with E. As the perturbation is increased, its invariant tori begin to break up, leading to more escape orbit and possible decrease of the KS entropy. The criterion obtained in Ref. [3] for the existence of invariant tori, E > D(A)1/3, seems to be available over a larger range than was established in that paper.

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