向量场奇异点的李亚普诺夫稳定性问题中的集合论病理
IF 1.4
3区 数学
Q1 MATHEMATICS
引用次数: 0
摘要
我们证明了李亚普诺夫稳定性问题甚至在集合论层面上也表现出了病态。也就是说，存在一个向量场 5 射流的解析单参数族，它通过一个不相交区间的可数联合与稳定射流集交叉。本文章由计算机程序翻译，如有差异，请以英文原文为准。
Set theoretical pathologies in the problem of Lyapunov stability of singular points of vector fields
We prove that Lyapunov stability problem demonstrates pathologies even on the set-theoretical level. Namely, there exists an analytic one-parameter family of 5-jets of vector fields that crosses the set of stable jets by a countable union of disjoint intervals.
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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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