{"title":"Local convexity for second order differential equations on a Lie algebroid","authors":"J. Marrero, D. D. Diego, E. Mart'inez","doi":"10.3934/jgm.2021021","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>A theory of local convexity for a second order differential equation (${\\text{sode}}$) on a Lie algebroid is developed. The particular case when the ${\\text{sode}}$ is homogeneous quadratic is extensively discussed.</p>","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"4 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Geometric Mechanics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/jgm.2021021","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 4
Abstract
A theory of local convexity for a second order differential equation (${\text{sode}}$) on a Lie algebroid is developed. The particular case when the ${\text{sode}}$ is homogeneous quadratic is extensively discussed.
期刊介绍：
The Journal of Geometric Mechanics (JGM) aims to publish research articles devoted to geometric methods (in a broad sense) in mechanics and control theory, and intends to facilitate interaction between theory and applications. Advances in the following topics are welcomed by the journal:
1. Lagrangian and Hamiltonian mechanics
2. Symplectic and Poisson geometry and their applications to mechanics
3. Geometric and optimal control theory
4. Geometric and variational integration
5. Geometry of stochastic systems
6. Geometric methods in dynamical systems
7. Continuum mechanics
8. Classical field theory
9. Fluid mechanics
10. Infinite-dimensional dynamical systems
11. Quantum mechanics and quantum information theory
12. Applications in physics, technology, engineering and the biological sciences.
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