PERIOD DOUBLING RENORMALIZATION FOR AREA-PRESERVING MAPS AND MILD COMPUTER ASSISTANCE IN CONTRACTION MAPPING PRINCIPLE
نویسندگان
چکیده
منابع مشابه
Period Doubling Renormalization for Area-Preserving Maps and Mild Computer Assistance in Contraction Mapping Principle
A universal period doubling cascade analogous to the famous FeigenbaumCoullet-Tresser period doubling has been observed in area-preserving maps of R. Existence of the “universal” map with orbits of all binary periods has been proved via a renormalization approach in (Eckmann et al 1984) and (Gaidashev et al 2011). These proofs use “hard” computer assistance. In this paper we attempt to reduce c...
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We study the critical behavior of period doublings in N symmetrically coupled area-preserving maps for many-coupled cases withN > 3. It is found that the critical scaling behaviors depend on the range of coupling interaction. In the extreme long-range case of global coupling, in which each area-preserving map is coupled to all the other area-preserving maps with equal strength, there exist an i...
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متن کاملPeriod Doubling in Area-Preserving Maps: An Associated One Dimensional Problem
It has been observed that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of R. A renormalization approach has been used in a computer-assisted proof of existence of an area-preserving map with orbits of all binary periods in [EKW1] and [EKW2]. As it is the case with all non-trivial universality problems in non-dissipative systems in...
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ژورنال
عنوان ژورنال: International Journal of Bifurcation and Chaos
سال: 2011
ISSN: 0218-1274,1793-6551
DOI: 10.1142/s0218127411030477