## 109 Citations

Symplectic rigidity for Anosov hypersurfaces

- MathematicsErgodic Theory and Dynamical Systems
- 2006

We prove that for a suitable (open) class of open, smoothly bounded domains in the cotangent bundle of a surface of genus $g \geq 2$ any exact symplectomorphism is homotopic to one which is smooth up…

Contact orderability up to conjugation

- Mathematics
- 2017

We study in this paper the remnants of the contact partial order on the orbits of the adjoint action of contactomorphism groups on their Lie algebras. Our main interest is a class of noncompact…

Spectrum estimates of Hill's lunar problem

- Physics, Mathematics
- 2015

We investigate the action spectrum of Hill's lunar problem by observing inclusions between the Liouville domains enclosed by the regularized energy hypersurfaces of the rotating Kepler problem and…

The solid trefoil knot as an algebraic surface

- Mathematics
- 2010

We give an explicit polynomial of degree 14 in three real variables x, y and z such that the zero set gives the solid trefoil knot. The polynomial depends on two further parameters which enable a…

Holomorphic curves and Hamiltonian systems in an open set with restricted contact-type boundary

- Mathematics
- 2000

On symplectic folding

- Mathematics
- 1999

We study the rigidity and flexibility of symplectic embeddings of simple shapes. It is first proved that under the condition $r_n^2 \le 2 r_1^2$ the symplectic ellipsoid $E(r_1, ..., r_n)$ with radii…

Symplectic and contact differential graded algebras

- Mathematics
- 2015

We define Hamiltonian simplex differential graded algebras (DGA) with differentials that deform the high energy symplectic homology differential and wrapped Floer homology differential in the cases…

The geometry of symplectic energy

- Mathematics
- 1993

"Non-Squeezing Theorem" which says that it is impossible to embed a large ball symplectically into a thin cylinder of the form R2, x B2, where B2 is a 2-disc. This led to Hofer's discovery of…

On the Lagrangian capacity of convex or concave toric domains

- Mathematics
- 2022

We establish computational results concerning the Lagrangian capacity, originally defined by Cieliebak–Mohnke. More precisely, we show that the Lagrangian capacity of a 4-dimensional convex toric…

Selective symplectic homology with applications to contact non-squeezing

- Mathematics
- 2022

We prove a contact non-squeezing phenomenon on homotopy spheres that are ﬁllable by Liouville domains with inﬁnite dimensional symplectic homology: there exists a smoothly embedded ball in such a…

## References

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Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations

- Mathematics
- 1984

An index theory for flows is presented which extends the classical Morse theory for gradient flows on compact manifolds. The theory is used to prove a Morse-type existence statement for periodic…

Pseudo holomorphic curves in symplectic manifolds

- Mathematics
- 1985

Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called…

Symplectic topology and Hamiltonian dynamics

- Physics, Mathematics
- 1988

On etudie des applications symplectiques non lineaires. Capacites symplectiques. Construction d'une capacite symplectique. Problemes de plongement. Problemes de rigidite

On the topological properties of symplectic maps

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 1990

Synopsis In this paper we show that symplectic maps have surprising topological properties. In particular, we construct an interesting metric for the symplectic diffeomorphism groups, which is…