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The Anosov-Katok method and pseudo-rotations in symplectic dynamics
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In this paper, it was shown that toric symplectic manifolds admit Hamiltonian pseudo-rotations with a finite, and in a sense minimal, number of ergodic measures.Abstract:
We prove that toric symplectic manifolds admit Hamiltonian pseudo-rotations with a finite, and in a sense minimal, number of ergodic measures. The set of ergodic measures of these pseudo-rotations consists of the measure induced by the symplectic volume form and the Dirac measures supported at the fixed points of the torus action. Our construction relies on the conjugation method of Anosov and Katok.read more
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Symplectic topology and hamiltonian dynamics
Ivar Ekeland,Helmut Hofer +1 more
TL;DR: On etudie des applications symplectiques non lineaires as discussed by the authors, construction d'une capacite symplectique, Problemes de plongement, and Probleme de rigidite
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Pseudo-rotations and holomorphic curves
TL;DR: In this paper, a variant of the Chance-McDuff conjecture for pseudo-rotations was proved for a manifold with weakly monotone and minimal Chern number at least two.
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The Calabi invariant for Hamiltonian diffeomorphisms of the unit disk
TL;DR: In this article, the Calabi invariant on the unit disk is extended to the group of diffeomorphisms of the closed disk which preserve the standard symplectic form, and the authors also compute the invariant for some diffeomorphic groups of the disk which satisfy some rigidity hypothesis.
On the growth of the Floer barcode
TL;DR: It is proved that in dimension two the sequential bar code entropy equals the topological entropy and hence equals the ordinary barcode entropy.
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A Hölder-Type Inequality for the C0 Distance and Anosov–Katok Pseudo-Rotations
TL;DR: In this paper , the authors prove a Hölder-type inequality for Hamiltonian diffeomorphisms relating the $C^0$ norm, the ε norm of the derivative, and the Hofer/spectral norm.
References
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Convexity and Commuting Hamiltonians
TL;DR: In this article, the adjoint action of G on its Lie algebra L(G) was considered and it was shown that W-orbits in L(T) correspond to G-orbit in L (G).
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Convexity properties of the moment mapping. II
TL;DR: The main result of as discussed by the authors is a description of the orbit structure of a set of co-adjoint orbits in a Caf tan subalgebra of g and a positive-definite G-invariant bilinear form on $.
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Introduction to the h-Principle
Yakov Eliashberg,N. Mishachev +1 more
TL;DR: The homotopy principle in symplectic geometry: Symplectic and contact structures on open manifold and contact structure on closed manifolds Embeddings into symplectic or contact manifolds Microflexibility and holonomic $\mathcal{R}$-approximation First applications of microflexibility Microflexible $mathfrak{U})-invariant differential relations Further applications to symplectic geometrical geometry Convex integration: One-dimensional convex integration Homotopy principles for ample differential relations Directed immersions and embeddings First order linear differential operators
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Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces
TL;DR: In this article, the Duistermaat-Heckman theorem multiplicities as invariants of reduced spaces partition functions are defined and examples of Kaehler structures on toric varieties.
Journal ArticleDOI
Symplectic topology and Hamiltonian dynamics
Ivar Ekeland,Helmut Hofer +1 more
TL;DR: On etudie des applications symplectiques non lineaires as mentioned in this paper, construction d'une capacite symplectique, Problemes de plongement, and Probleme de rigidite