Transverse foliations in the rotating Kepler problem
IF 1.4
3区 数学
Q1 MATHEMATICS
引用次数: 0
Abstract
We construct finite energy foliations and transverse foliations of neighbourhoods of the circular orbits in the rotating Kepler problem for all negative energies. This paper would be a first step towards our ultimate goal that is to recover and refine McGehee’s results on homoclinics [23] and to establish a theoretical foundation to the numerical demonstration of the existence of a homoclinic–heteroclinic chain in the planar circular restricted three-body problem [20], using pseudoholomorphic curves.
旋转开普勒问题中的横切面
我们构建了开普勒旋转问题中所有负能量的圆轨道邻域的有限能量叶形和横向叶形。本文将是实现我们最终目标的第一步，即恢复和完善麦格希（McGehee）关于同次圆的结果[23]，并为在平面圆受限三体问题[20]中利用伪同次圆曲线数值证明同次圆-异次圆链的存在奠定理论基础。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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来源期刊
CiteScore
3.10
自引率
5.60%
发文量
68
审稿时长
>12 weeks
期刊介绍：
The Journal of Fixed Point Theory and Applications (JFPTA) provides a publication forum for an important research in all disciplines in which the use of tools of fixed point theory plays an essential role. Research topics include but are not limited to:
(i) New developments in fixed point theory as well as in related topological methods,
in particular:
Degree and fixed point index for various types of maps,
Algebraic topology methods in the context of the Leray-Schauder theory,
Lefschetz and Nielsen theories,
Borsuk-Ulam type results,
Vietoris fractions and fixed points for set-valued maps.
(ii) Ramifications to global analysis, dynamical systems and symplectic topology,
in particular:
Degree and Conley Index in the study of non-linear phenomena,
Lusternik-Schnirelmann and Morse theoretic methods,
Floer Homology and Hamiltonian Systems,
Elliptic complexes and the Atiyah-Bott fixed point theorem,
Symplectic fixed point theorems and results related to the Arnold Conjecture.
(iii) Significant applications in nonlinear analysis, mathematical economics and computation theory,
in particular:
Bifurcation theory and non-linear PDE-s,
Convex analysis and variational inequalities,
KKM-maps, theory of games and economics,
Fixed point algorithms for computing fixed points.
(iv) Contributions to important problems in geometry, fluid dynamics and mathematical physics,
in particular:
Global Riemannian geometry,
Nonlinear problems in fluid mechanics.
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