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A survey on local integrability and its regularity
Authors: Yantao Yang and Xiang Zhang
Keywords: Analytic differential systems, integrability, regularity, Gevrey smoothness, normalization
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Keywords: Analytic differential systems, integrability, regularity, Gevrey smoothness, normalization
Abstract
In this survey paper, we summarize our results and also some related ones on local integrability of analytic autonomous differential systems near an equilibrium. The results are on necessary conditions related to existence of local analytic or meromorphic first integrals, on existence of analytic normalization of local analytically integrable system, and also on some sufficient conditions for existence of local analytic first integrals. Among which the results are also on regularity of the local first integrals, including analytic and Gevrey smoothness. We also present some open questions for further investigation.Yantao Yang
College of Mathematics and Computer Science, Yanan
University, Yanan 716000, Shaanxi, People’s Republic of
China
E-mail:
Xiang Zhang
School of Mathematical Sciences, MOE–LSC, and
CAM-Shanghai, Shanghai Jiao Tong University, Shanghai
200240, People’s Republic of China
E-mail:
College of Mathematics and Computer Science, Yanan
University, Yanan 716000, Shaanxi, People’s Republic of
China
E-mail:
Xiang Zhang
School of Mathematical Sciences, MOE–LSC, and
CAM-Shanghai, Shanghai Jiao Tong University, Shanghai
200240, People’s Republic of China
E-mail:
DOI
https://doi.org/10.56415/basm.y2023.i1.p29Fulltext
– 0.15 Mb
Contents
- Criteria for the nonexistence of periodic orbits in planar differential systems
- Some families of quadratic systems with at most one limit cycle
- Time-Reversibility and Ivariants of Some 3-dim Systems
- A survey on local integrability and its regularity
- The bifurcation diagram of the configurations of invariant lines of total multiplicity exactly three in quadratic vector fields
- Counting configurations of limit cycles and centers
