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Dirac constraints in field theory and exterior differential systems
Geodesic boundary value problems with symmetry
1.  Department of Aeronautics, Imperial College London, London SW7 2AZ, United Kingdom 
2.  Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom 
[1] 
Alex Eskin, Maryam Mirzakhani. Counting closed geodesics in moduli space. Journal of Modern Dynamics, 2011, 5 (1) : 71105. doi: 10.3934/jmd.2011.5.71 
[2] 
R. Bartolo, Anna Maria Candela, J.L. Flores. Timelike Geodesics in stationary Lorentzian manifolds with unbounded coefficients. Conference Publications, 2005, 2005 (Special) : 7076. doi: 10.3934/proc.2005.2005.70 
[3] 
Samir Chowdhury, Facundo Mémoli. Explicit geodesics in GromovHausdorff space. Electronic Research Announcements, 2018, 25: 4859. doi: 10.3934/era.2018.25.006 
[4] 
Martin Bauer, Philipp Harms, Peter W. Michor. Sobolev metrics on shape space of surfaces. Journal of Geometric Mechanics, 2011, 3 (4) : 389438. doi: 10.3934/jgm.2011.3.389 
[5] 
E. GarcíaToraño Andrés, Bavo Langerock, Frans Cantrijn. Aspects of reduction and transformation of Lagrangian systems with symmetry. Journal of Geometric Mechanics, 2014, 6 (1) : 123. doi: 10.3934/jgm.2014.6.1 
[6] 
Keith Burns, Eugene Gutkin. Growth of the number of geodesics between points and insecurity for Riemannian manifolds. Discrete and Continuous Dynamical Systems, 2008, 21 (2) : 403413. doi: 10.3934/dcds.2008.21.403 
[7] 
Giovanni De Matteis, Gianni Manno. Lie algebra symmetry analysis of the Helfrich and Willmore surface shape equations. Communications on Pure and Applied Analysis, 2014, 13 (1) : 453481. doi: 10.3934/cpaa.2014.13.453 
[8] 
Anant A. Joshi, D. H. S. Maithripala, Ravi N. Banavar. A bundle framework for observer design on smooth manifolds with symmetry. Journal of Geometric Mechanics, 2021, 13 (2) : 247271. doi: 10.3934/jgm.2021015 
[9] 
Jan J. Dijkstra and Jan van Mill. Homeomorphism groups of manifolds and Erdos space. Electronic Research Announcements, 2004, 10: 2938. 
[10] 
L. Búa, T. Mestdag, M. Salgado. Symmetry reduction, integrability and reconstruction in $k$symplectic field theory. Journal of Geometric Mechanics, 2015, 7 (4) : 395429. doi: 10.3934/jgm.2015.7.395 
[11] 
Claudio Meneses. Linear phase space deformations with angular momentum symmetry. Journal of Geometric Mechanics, 2019, 11 (1) : 4558. doi: 10.3934/jgm.2019003 
[12] 
Hui Liu, Yiming Long, Yuming Xiao. The existence of two noncontractible closed geodesics on every bumpy Finsler compact space form. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 38033829. doi: 10.3934/dcds.2018165 
[13] 
Jeffrey K. Lawson, Tanya Schmah, Cristina Stoica. EulerPoincaré reduction for systems with configuration space isotropy. Journal of Geometric Mechanics, 2011, 3 (2) : 261275. doi: 10.3934/jgm.2011.3.261 
[14] 
Holger R. Dullin, Jürgen Scheurle. Symmetry reduction of the 3body problem in $ \mathbb{R}^4 $. Journal of Geometric Mechanics, 2020, 12 (3) : 377394. doi: 10.3934/jgm.2020011 
[15] 
Sebastián Ferrer, Francisco Crespo. Alternative anglebased approach to the $\mathcal{KS}$Map. An interpretation through symmetry and reduction. Journal of Geometric Mechanics, 2018, 10 (3) : 359372. doi: 10.3934/jgm.2018013 
[16] 
Martin Bauer, Philipp Harms, Peter W. Michor. Sobolev metrics on shape space, II: Weighted Sobolev metrics and almost local metrics. Journal of Geometric Mechanics, 2012, 4 (4) : 365383. doi: 10.3934/jgm.2012.4.365 
[17] 
Matteo Novaga, Diego Pallara, Yannick Sire. A symmetry result for degenerate elliptic equations on the Wiener space with nonlinear boundary conditions and applications. Discrete and Continuous Dynamical Systems  S, 2016, 9 (3) : 815831. doi: 10.3934/dcdss.2016030 
[18] 
Margarida Camarinha, Fátima Silva Leite, Peter Crouch. Riemannian cubics close to geodesics at the boundaries. Journal of Geometric Mechanics, 2022 doi: 10.3934/jgm.2022003 
[19] 
Alexander Nabutovsky and Regina Rotman. Lengths of geodesics between two points on a Riemannian manifold. Electronic Research Announcements, 2007, 13: 1320. 
[20] 
Eva Glasmachers, Gerhard Knieper, Carlos Ogouyandjou, Jan Philipp Schröder. Topological entropy of minimal geodesics and volume growth on surfaces. Journal of Modern Dynamics, 2014, 8 (1) : 7591. doi: 10.3934/jmd.2014.8.75 
2020 Impact Factor: 0.857
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