Keyword

Dirac structures

Description: Dirac structures are geometric structures combining tangent and cotangent information, used to describe constrained dynamics and interconnections in mathematical physics.

Primary topic: Homotopy and Cohomology in Algebraic Topology (26%)

Wikidata ID: wiki/Q117751500

OpenAlex ID: keywords/dirac-structures

Dirac Manifolds

1990 · Theodore James Courant · Transactions of the American Mathematical Society · 660

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Manin triples for Lie bialgebroids

1997 · Zhang-Ju Liu, Alan Weinstein, et al. · Journal of Differential Geometry · 570

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Hamiltonian formulation of distributed-parameter systems with boundary energy flow

2002 · A.J. van der Schaft, B.M. Maschke · Journal of Geometry and Physics · 531

Dirac Structures and Integrability of Nonlinear Evolution Equations

1993 · I. Ya. Dorfman · 443

Poisson Geometry with a 3-Form Background

2001 · Pavol Ševera, Alan Weinstein · Progress of Theoretical Physics Supplement · 371

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Dirac structures and Boundary Control Systems associated with Skew-Symmetric Differential Operators

2005 · Y. Le Gorrec, H. Zwart, et al. · SIAM Journal on Control and Optimization · 306

On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems

1998 · Morten Dalsmo, Arjan van der Schaft · SIAM Journal on Control and Optimization · 280

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The Hamiltonian formulation of energy conserving physical systems with external ports

1995 · Arjan van der Schaft, Bernhard Maschke · University of Twente Research Information · 274

Reduction of Courant algebroids and generalized complex structures

2006 · Henrique Bursztyn, Gil R. Cavalcanti, et al. · Advances in Mathematics · 242

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Port-Hamiltonian systems: an introductory survey

2007 · Arjan van der Schaft · Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006 · 223

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Port-Hamiltonian Systems on Graphs

2013 · A. J. van der Schaft, B. M. Maschke · SIAM Journal on Control and Optimization · 181

Dirac structures in Lagrangian mechanics Part I: Implicit Lagrangian systems

2006 · Hiroaki Yoshimura, Jerrold E. Marsden · Journal of Geometry and Physics · 175

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Interconnection of port-Hamiltonian systems and composition of Dirac structures

2006 · J. Cervera, A.J. van der Schaft, et al. · Automatica · 159

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Dirac structures of integrable evolution equations

1987 · Irene Ya. Dorfman · Physics Letters A · 152

The Breadth of Symplectic and Poisson Geometry

2007 · Marsden, Jerrold E, Ratiu, Tudor S · Birkhäuser Boston eBooks · 138

Dirac structures in Lagrangian mechanics Part II: Variational structures

2006 · Hiroaki Yoshimura, Jerrold E. Marsden · Journal of Geometry and Physics · 125

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Current Algebra and Differential Geometry

2005 · Anton Alekseev, Thomas Strobl · Journal of High Energy Physics · 112

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Generalized complex geometry and T-duality

2010 · Gil Cavalcanti, Marco Gualtieri · CRM proceedings & lecture notes · 109

Courant Algebroids and Strongly Homotopy Lie Algebras

1998 · Roytenberg, Dmitry, Weinstein, Alan · arXiv (Cornell University) · 107

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Gauge equivalence of Dirac structures and symplectic groupoids

2003 · Henrique Bursztyn, Olga Radko · Annales de l’institut Fourier · 105

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Generalized Kähler Geometry

2014 · Marco Gualtieri · Communications in Mathematical Physics · 102

Poisson vertex algebras in the theory of Hamiltonian equations

2009 · Aliaa Barakat, Alberto De Sole, et al. · Japanese journal of mathematics · 102

On the geometry of double field theory

2012 · Izu Vaisman · Journal of Mathematical Physics · 101

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Representations up to homotopy of Lie algebroids

2011 · Camilo Arias Abad, Marius Crainic · Journal für die reine und angewandte Mathematik (Crelles Journal) · 100

Poisson vertex algebras in the theory of Hamiltonian equations

2009 · Aliaa Barakat, Alberto De Sole, et al. · 100

Works count: 800

Citation count: 11,840