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HAT: Hamiltonian Systems—Applications and Theory
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Dr. Alessandro Bravetti
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A.P. 70-543, Ciudad de México 04510, Mexico
Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Calle Nicolás Cabrera, 13-15, Campus Cantoblanco, UAM, 28049 Madrid, Spain
Dr. Ángel Alejandro García-Chung
1. Departamento de Física, Universidad Autónoma Metropolitana—Iztapalapa, San Rafael Atlixco 186, Ciudad de México 09340, México
2. Tecnológico de Monterrey, Escuela de Ingeniería y Ciencias, Carr. al Lago de Guadalupe Km. 3.5, Estado de Mexico 52926, Mexico
Dr. Marcello Seri
Bernoulli Insitute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, 9700 AK Groningen, The Netherlands
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HAT: Hamiltonian Systems—Applications and Theory

Abstract submission deadline
closed (30 August 2023)
Manuscript submission deadline
closed (30 December 2023)
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3274

Topic Information

Dear Colleagues,

Hamiltonian systems have been one of the most influential ideas in the theory of dynamical systems and in the formulation of physical theories ever since their discovery by J. L. Lagrange and W. R. Hamilton. Due to their appealing theoretical properties, they are a central node at the intersection of topology, geometry and dynamical systems. Moreover, they are being used to lay the foundations of an ever-growing number of applications that span from classical and quantum mechanics to statistical physics and general relativity, from chemical reactions to thermodynamics, and from evolutionary game theory to models of biological evolution and data science. The flourishing of so many different fields of application has, in turn, increased the number of relevant questions that must be addressed about these systems. The result is that there is currently so much investigation going on concerning Hamiltonian systems and their Lagrangian counterparts that it is hard—if not impossible—to keep track of all the new questions and results appearing in the literature, and there is a pressing need for synthesis of all these directions. The aim of this Topic is to provide an opportunity to anyone interested in Hamiltonian systems, from very different perspectives, to join their works together as part of a collection, which will take a broad as well as unified view of the state of the art regarding the knowledge on Hamiltonian systems with regard to both theory and applications.

Dr. Alessandro Bravetti
Prof. Dr. Manuel De León
Dr. Ángel Alejandro García-Chung
Dr. Marcello Seri
Topic Editors

Keywords

  • hamiltonian systems
  • Lagrangian dynamics
  • symplectic geometry
  • contact geometry
  • Poisson geometry
  • Jacobi geometry
  • integrable systems
  • KAM theory
  • perturbation theory
  • hamiltonian PDEs
  • geometric numerical integration
  • optimal control
  • geometric mechanics
  • constrained Hamiltonian systems
  • quantization
  • hamiltonian formulation of general relativity
  • hamiltonian thermodynamics
  • roaming reaction dynamics
  • hamiltonian monte carlo
  • hamiltonian neural networks
  • hamiltonian optimization
  • hamiltonian games

Participating Journals

Journal Name Impact Factor CiteScore Launched Year First Decision (median) APC
Entropy
entropy 		2.7 4.7 1999 20.8 Days CHF 2600
Fractal and Fractional
fractalfract 		5.4 3.6 2017 18.9 Days CHF 2700
Mathematical and Computational Applications
mca 		1.9 - 1996 22.5 Days CHF 1400
Mathematics
mathematics 		2.4 3.5 2013 16.9 Days CHF 2600
Symmetry
symmetry 		2.7 4.9 2009 16.2 Days CHF 2400

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Published Papers (1 paper)

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14 pages, 307 KiB  
Article
The Number of Limit Cycles Bifurcating from an Elementary Centre of Hamiltonian Differential Systems
by Lijun Wei, Yun Tian and Yancong Xu
Mathematics 2022, 10(9), 1483; https://doi.org/10.3390/math10091483 - 29 Apr 2022
Viewed by 1241
Abstract
This paper studies the number of small limit cycles produced around an elementary center for Hamiltonian differential systems with the elliptic Hamiltonian function [...] Read more.
This paper studies the number of small limit cycles produced around an elementary center for Hamiltonian differential systems with the elliptic Hamiltonian function H=12y2+12x2−23x3+a4x4(a≠0) under two types of polynomial perturbations of degree m, respectively. It is proved that the Hamiltonian system perturbed in Liénard systems can have at least [3m−14] small limit cycles near the center, where m≤101, and that the related near-Hamiltonian system with general polynomial perturbations can have at least m+[m+12]−2 small-amplitude limit cycles, where m≤16. Furthermore, in any of the cases, the bounds for limit cycles can be reached by studying the isolated zeros of the corresponding first order Melnikov functions and with the help of Maple programs. Here, [·] represents the integer function. Full article
(This article belongs to the Topic HAT: Hamiltonian Systems—Applications and Theory)
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