No elliptic islands for the universal area-preserving map
نویسندگان
چکیده
منابع مشابه
Dynamics of the Universal Area-preserving Map Associated with Period Doubling: Stable Sets
It is known 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 (Eckmann et al 1982) and (Eckmann et al 1984) in a computer-assisted proof of existence of a “universal” areapreserving map F∗ — a map with orbits of all binary periods 2 , k ∈ N. In this paper, we consider infinitely re...
متن کاملDynamics of the Universal Area-Preserving Map Associated with Period Doubling: Hyperbolic Sets
It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of R2. A renormalization approach has been used in (Eckmann et al 1982) and (Eckmann et al 1984) in a computer-assisted proof of existence of a “universal” area-preserving map F∗ — a map with orbits of all binary periods 2k, k ∈ N. In this paper, we consider maps in som...
متن کاملConformal maps and non-reversibility of elliptic area-preserving maps
It has been long observed that area-preserving maps and reversible maps share similar results. This was certainly known to G.D. Birkhoff [5] who showed that these two types of maps have periodic orbits near a general elliptic fixed point. The KAM theory, developed by Kolmogorov-ArnoldMoser for Hamiltonian systems [9], [1] and area preserving maps [15], has also been extended a great deal to rev...
متن کاملCharacteristics of a piecewise smooth area-preserving map.
We are reporting a study carried out in a system concatenated by two area-preserving maps. The system can be viewed as a model of an electronic relaxation oscillator with over-voltage protection. We found that a border-collision bifurcation may interrupt a period-doubling bifurcation cascade, and that some special features, such as "quasicoexisting periodic orbits crossing border" as well as th...
متن کاملA Bound for the Fixed-Point Index of an Area-Preserving Map with Applications to Mechanics
Area-preserving maps and flows play an essential role in the study of motions of mechanical systems, especially in celestial mechanics (see [1, 14]). Since one is often interested in the behavior of an area-preserving map around a fixed point and in the number and type of critical points and periodic orbits of an area-preserving flow, the ./i'xed-point index of a map and the index oj" a singula...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2011
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/24/7/008