# Singular Hamiltonian systems and symplectic capacities

Banach Center Publications (1996)

- Volume: 33, Issue: 1, page 171-187
- ISSN: 0137-6934

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topKünzle, Alfred. "Singular Hamiltonian systems and symplectic capacities." Banach Center Publications 33.1 (1996): 171-187. <http://eudml.org/doc/262540>.

@article{Künzle1996,

abstract = {The purpose of this paper is to develop the basics of a theory of Hamiltonian systems with non-differentiable Hamilton functions which have become important in symplectic topology. A characteristic differential inclusion is introduced and its equivalence to Hamiltonian inclusions for certain convex Hamiltonians is established. We give two counterexamples showing that basic properties of smooth systems are violated for non-smooth quasiconvex submersions, e.g. even the energy conservation which nevertheless holds for convex submersions. This also implies that the convexity assumption determines, although not symplectically invariant, a limit case for symplectic geometry. Some applications of this theory are reviewed: symplectic capacities for general convex sets, the symplectic product and a product formula for symplectic capacities.},

author = {Künzle, Alfred},

journal = {Banach Center Publications},

keywords = {symplectic capacity; differential inclusion; singular Hamiltonian},

language = {eng},

number = {1},

pages = {171-187},

title = {Singular Hamiltonian systems and symplectic capacities},

url = {http://eudml.org/doc/262540},

volume = {33},

year = {1996},

}

TY - JOUR

AU - Künzle, Alfred

TI - Singular Hamiltonian systems and symplectic capacities

JO - Banach Center Publications

PY - 1996

VL - 33

IS - 1

SP - 171

EP - 187

AB - The purpose of this paper is to develop the basics of a theory of Hamiltonian systems with non-differentiable Hamilton functions which have become important in symplectic topology. A characteristic differential inclusion is introduced and its equivalence to Hamiltonian inclusions for certain convex Hamiltonians is established. We give two counterexamples showing that basic properties of smooth systems are violated for non-smooth quasiconvex submersions, e.g. even the energy conservation which nevertheless holds for convex submersions. This also implies that the convexity assumption determines, although not symplectically invariant, a limit case for symplectic geometry. Some applications of this theory are reviewed: symplectic capacities for general convex sets, the symplectic product and a product formula for symplectic capacities.

LA - eng

KW - symplectic capacity; differential inclusion; singular Hamiltonian

UR - http://eudml.org/doc/262540

ER -

## References

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