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Volume 12, 2020

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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


Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.

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Preface to the special issue dedicated to James Montaldi
Luis C. García-Naranjo, Manuel de León and Juan Pablo Ortega
2020, 12(3) : ⅰ-ⅳ doi: 10.3934/jgm.2020028 +[Abstract](180) +[HTML](71) +[PDF](2018.06KB)
Relative equilibria of the 3-body problem in $ \mathbb{R}^4 $
Alain Albouy and Holger R. Dullin
2020, 12(3) : 323-341 doi: 10.3934/jgm.2020012 +[Abstract](657) +[HTML](377) +[PDF](1229.84KB)
The method of averaging for Poisson connections on foliations and its applications
Misael Avendaño-Camacho, Isaac Hasse-Armengol, Eduardo Velasco-Barreras and Yury Vorobiev
2020, 12(3) : 343-361 doi: 10.3934/jgm.2020015 +[Abstract](449) +[HTML](179) +[PDF](374.4KB)
The group of symplectic birational maps of the plane and the dynamics of a family of 4D maps
Inês Cruz, Helena Mena-Matos and Esmeralda Sousa-Dias
2020, 12(3) : 363-375 doi: 10.3934/jgm.2020010 +[Abstract](820) +[HTML](303) +[PDF](351.75KB)
Symmetry reduction of the 3-body problem in $ \mathbb{R}^4 $
Holger R. Dullin and Jürgen Scheurle
2020, 12(3) : 377-394 doi: 10.3934/jgm.2020011 +[Abstract](583) +[HTML](309) +[PDF](473.96KB)
Control of locomotion systems and dynamics in relative periodic orbits
Francesco Fassò, Simone Passarella and Marta Zoppello
2020, 12(3) : 395-420 doi: 10.3934/jgm.2020022 +[Abstract](239) +[HTML](113) +[PDF](763.92KB)
Higher order normal modes
Giuseppe Gaeta and Sebastian Walcher
2020, 12(3) : 421-434 doi: 10.3934/jgm.2020026 +[Abstract](170) +[HTML](74) +[PDF](403.94KB)
Some remarks about the centre of mass of two particles in spaces of constant curvature
Luis C. García-Naranjo
2020, 12(3) : 435-446 doi: 10.3934/jgm.2020020 +[Abstract](255) +[HTML](122) +[PDF](595.46KB)
Characterization of toric systems via transport costs
Sonja Hohloch
2020, 12(3) : 447-454 doi: 10.3934/jgm.2020027 +[Abstract](180) +[HTML](68) +[PDF](308.99KB)
Angular momentum coupling, Dirac oscillators, and quantum band rearrangements in the presence of momentum reversal symmetries
Toshihiro Iwai, Dmitrií A. Sadovskií and Boris I. Zhilinskií
2020, 12(3) : 455-505 doi: 10.3934/jgm.2020021 +[Abstract](273) +[HTML](130) +[PDF](740.58KB)
Getting into the vortex: On the contributions of james montaldi
Jair Koiller
2020, 12(3) : 507-523 doi: 10.3934/jgm.2020018 +[Abstract](191) +[HTML](91) +[PDF](1542.0KB)
Continuous singularities in hamiltonian relative equilibria with abelian momentum isotropy
Miguel Rodríguez-Olmos
2020, 12(3) : 525-540 doi: 10.3934/jgm.2020019 +[Abstract](243) +[HTML](127) +[PDF](339.64KB)
A summary on symmetries and conserved quantities of autonomous Hamiltonian systems
Narciso Román-Roy
2020, 12(3) : 541-551 doi: 10.3934/jgm.2020009 +[Abstract](579) +[HTML](317) +[PDF](349.98KB)
Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics
Manuel de León, Juan Carlos Marrero and David Martín de Diego
2010, 2(2) : 159-198 doi: 10.3934/jgm.2010.2.159 +[Abstract](3635) +[PDF](475.8KB) Cited By(43)
Sobolev metrics on shape space of surfaces
Martin Bauer, Philipp Harms and Peter W. Michor
2011, 3(4) : 389-438 doi: 10.3934/jgm.2011.3.389 +[Abstract](3877) +[PDF](2091.6KB) Cited By(31)
Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle
Joachim Escher and Boris Kolev
2014, 6(3) : 335-372 doi: 10.3934/jgm.2014.6.335 +[Abstract](2986) +[PDF](587.5KB) Cited By(25)
On Euler's equation and 'EPDiff'
David Mumford and Peter W. Michor
2013, 5(3) : 319-344 doi: 10.3934/jgm.2013.5.319 +[Abstract](3603) +[PDF](661.6KB) Cited By(24)
Geodesic Vlasov equations and their integrable moment closures
Darryl D. Holm and Cesare Tronci
2009, 1(2) : 181-208 doi: 10.3934/jgm.2009.1.181 +[Abstract](3178) +[PDF](360.8KB) Cited By(22)
Nonholonomic Hamilton-Jacobi equation and integrability
Tomoki Ohsawa and Anthony M. Bloch
2009, 1(4) : 461-481 doi: 10.3934/jgm.2009.1.461 +[Abstract](3216) +[PDF](789.5KB) Cited By(21)
Integrable Euler top and nonholonomic Chaplygin ball
Andrey Tsiganov
2011, 3(3) : 337-362 doi: 10.3934/jgm.2011.3.337 +[Abstract](2925) +[PDF](488.1KB) Cited By(20)
Clebsch optimal control formulation in mechanics
François Gay-Balmaz and Tudor S. Ratiu
2011, 3(1) : 41-79 doi: 10.3934/jgm.2011.3.41 +[Abstract](2956) +[PDF](597.2KB) Cited By(19)
Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations
Ioan Bucataru and Matias F. Dahl
2009, 1(2) : 159-180 doi: 10.3934/jgm.2009.1.159 +[Abstract](3606) +[PDF](318.8KB) Cited By(17)
Three-dimensional discrete systems of Hirota-Kimura type and deformed Lie-Poisson algebras
Andrew N. W. Hone and Matteo Petrera
2009, 1(1) : 55-85 doi: 10.3934/jgm.2009.1.55 +[Abstract](2816) +[PDF](494.1KB) Cited By(17)
Infinite dimensional integrals and partial differential equations for stochastic and quantum phenomena
Sergio Albeverio and Sonia Mazzucchi
2019, 11(2) : 123-137 doi: 10.3934/jgm.2019006 +[Abstract](4110) +[HTML](394) +[PDF](468.22KB) PDF Downloads(283)
Invariant metrics on Lie groups
Gerard Thompson
2015, 7(4) : 517-526 doi: 10.3934/jgm.2015.7.517 +[Abstract](2716) +[PDF](369.5KB) PDF Downloads(223)
Probability measures on infinite-dimensional Stiefel manifolds
Eleonora Bardelli and Andrea Carlo Giuseppe Mennucci
2017, 9(3) : 291-316 doi: 10.3934/jgm.2017012 +[Abstract](2252) +[HTML](58) +[PDF](609.1KB) PDF Downloads(180)
Riemannian cubics and elastica in the manifold $ \operatorname{SPD}(n) $ of all $ n\times n $ symmetric positive-definite matrices
Erchuan Zhang and Lyle Noakes
2019, 11(2) : 277-299 doi: 10.3934/jgm.2019015 +[Abstract](3874) +[HTML](319) +[PDF](1374.62KB) PDF Downloads(167)
Lagrange-d'alembert-poincaré equations by several stages
Hernán Cendra and Viviana A. Díaz
2018, 10(1) : 1-41 doi: 10.3934/jgm.2018001 +[Abstract](5838) +[HTML](459) +[PDF](622.49KB) PDF Downloads(164)
On the degenerate boussinesq equations on surfaces
Siran Li, Jiahong Wu and Kun Zhao
2020, 12(1) : 107-140 doi: 10.3934/jgm.2020006 +[Abstract](1323) +[HTML](249) +[PDF](703.04KB) PDF Downloads(163)
A summary on symmetries and conserved quantities of autonomous Hamiltonian systems
Narciso Román-Roy
2020, 12(3) : 541-551 doi: 10.3934/jgm.2020009 +[Abstract](579) +[HTML](317) +[PDF](349.98KB) PDF Downloads(158)
Conservation laws in discrete geometry
Len G. Margolin and Roy S. Baty
2019, 11(2) : 187-203 doi: 10.3934/jgm.2019010 +[Abstract](4165) +[HTML](306) +[PDF](382.02KB) PDF Downloads(155)
Classical field theory on Lie algebroids: Multisymplectic formalism
Eduardo Martínez
2018, 10(1) : 93-138 doi: 10.3934/jgm.2018004 +[Abstract](6706) +[HTML](544) +[PDF](708.21KB) PDF Downloads(151)
A note on time-optimal paths on perturbed spheroid
Piotr Kopacz
2018, 10(2) : 139-172 doi: 10.3934/jgm.2018005 +[Abstract](3906) +[HTML](328) +[PDF](3595.86KB) PDF Downloads(150)

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