Set theoretical pathologies in the problem of Lyapunov stability of singular points of vector fields

被引：0

作者：

Ilyashenko, Yu. ^{[1
,2
]}

机构：

[1] Natl Res Univ Higher Sch Econ, Moscow, Russia

[2] Independent Univ Moscow, Moscow, Russia

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2024年 / 26卷 / 02期

关键词：

lyapunov stability; stable jets; factor system; radial function;

D O I：

10.1007/s11784-024-01111-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：10

共 50 条

[1] Vector fields with a given set of singular points
A. O. Prishlyak
[J]. Ukrainian Mathematical Journal, 1997, 49 (10) : 1548 - 1558
[2] The problem of center for resonant singular points of polynomial vector fields
Zoladek, H
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 137 (01) : 94 - 118
[3] On the center problem for degenerate singular points of planar vector fields
Mañosa, V
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2002, 12 (04): : 687 - 707
[4] Conical Singular Points and Vector Fields
Burian, S. N.
[J]. VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS, 2021, 54 (04) : 311 - 320
[5] Vector fields with nonisolated singular points
Remizov, AO
[J]. DOKLADY MATHEMATICS, 2002, 65 (03) : 437 - 439
[6] Conical Singular Points and Vector Fields
S. N. Burian
[J]. Vestnik St. Petersburg University, Mathematics, 2021, 54 : 311 - 320
[7] SEPARATRICES AT SINGULAR POINTS OF PLANAR VECTOR-FIELDS
SCHECTER, S
SINGER, MF
[J]. ACTA MATHEMATICA, 1980, 145 (1-2) : 47 - 78
[8] Set of strictly efficient points of mixed integer vector optimization problem as a measure of problem's stability
Kozeratskaya, LN
[J]. CYBERNETICS AND SYSTEMS ANALYSIS, 1997, 33 (06) : 901 - 903
[9] Set of strictly efficient points of mixed integer vector optimization problem as a measure of problem’s stability
L. N. Kozeratskaya
[J]. Cybernetics and Systems Analysis, 1997, 33 : 901 - 903
[10] Newton diagrams, odd points, and the index of singular points of planar vector fields
I. V. Antyushina
N. M. Bliznyakov
[J]. Mathematical Notes, 2011, 89 : 757 - 760

← 1 2 3 4 5 →