Periodic expansion in determining minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms

被引：9

作者：

Graff, Grzegorz ^{[1
]}

Lebiedz, Malgorzata ^{[2
]}

Myszkowski, Adrian ^{[1
]}

机构：

[1] Gdansk Univ Technol, Fac Appl Phys & Math, Narutowicza 11-12, PL-80233 Gdansk, Poland

[2] Univ Gdansk, Inst Math, Wita Stwosza 57, PL-80952 Gdansk, Poland

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2019年 / 21卷 / 02期

关键词：

Morse-Smale diffeomorphism; Lefschetz number; periodic expansion; zeta function; set of periods; non-orientable compact surfaces; FIXED-POINT INDEXES; TRANSVERSAL MAPS; SELF-MAPS; NUMBER;

D O I：

10.1007/s11784-019-0680-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We apply the representation of Lefschetz numbers of iterates in the form of periodic expansion to determine the minimal sets of Lefschetz periods of Morse-Smale diffeomorphisms. Applying this approach we present an algorithmic method of finding the family of minimal sets of Lefschetz periods for Ng, a non-orientable compact surfaces without boundary of genus g. We also partially confirm the conjecture of Llibre and Sirvent (J Diff Equ Appl 19(3):402-417, 2013) proving that there are no algebraic obstacles in realizing any set of odd natural numbers as the minimal set of Lefschetz periods on Ng for any g.

引用

页数：21

共 34 条

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