Vladimir Igorevich Arnold and the Invention of Symplectic Topology

DOI10.1007/978-3-319-02036-5_1zbMath1333.53003OpenAlexW48715906MaRDI QIDQ2949883

Michèle Audin

Publication date: 5 October 2015

Published in: Bolyai Society Mathematical Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-02036-5_1

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) History of mathematics in the 21st century (01A61) Global theory of symplectic and contact manifolds (53D35) History of differential geometry (53-03) Schools of mathematics (01A72)

Related Items (4)

Poincaré-Birkhoff Theorems in random dynamics ⋮ Hamiltonian and symplectic symmetries: An introduction ⋮ Floer homologies, with applications ⋮ Three examples in the dynamical systems theory

Cites Work

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• V. I. Arnold (1937--2010)
• Points fixes d'une application symplectique homologue à l'identité
• Quelques calculs en corbordisme lagrangien
• A symplectic fixed point theorem for \({\mathbb{C}}P^ n\)
• In memory of Henri Cartan
• Lagrangian Klein bottles in \({\mathbb{R}^{2n}}\)
• The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold
• Pseudo holomorphic curves in symplectic manifolds
• Proof of the Arnold conjecture for surfaces and generalizations to certain Kähler manifolds
• Lagrangian imbeddings of surfaces and unfolded Whitney umbrella
• A theorem on the structure of wave fronts and its applications in symplectic topology
• On fixed points of symplectic maps
• Lagrange and Legendre cobordisms. II
• Convexity properties of the moment mapping
• Reduction of symplectic manifolds with symmetry
• On the hypotheses of Rabinowitz' periodic orbit theorems
• Proof of the Poincaré-Birkhoff fixed point theorem
• A symplectic fixed point theorem for complex projective spaces
• First steps in symplectic topology
• Convexity and Commuting Hamiltonians
• QUANTIZATION
• Symplectic v‐manifolds, periodic orbits of hamiltonian systems, and the volume of certain riemannian manifolds
• Corrigenda to: Introduction to Symplectic Topology
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
• On the Volume Elements on a Manifold

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