3 citations · 5 across the 6 of their papers we have counts for
10 papers
Twisted Morse complexes
Augustin Banyaga, David Hurtubise, Peter Spaeth
In this paper we study Morse homology and cohomology with local coefficients, i.e. "twisted" Morse homology and cohomology, on closed finite dimensional smooth manifolds. We prove…
The symplectic displacement energy
Augustin Banyaga, David E. Hurtubise, Peter Spaeth
We define the symplectic displacement energy of a non-empty subset of a compact symplectic manifold as the infimum of the Hofer-like norm [5] of symplectic diffeomorphisms that dis…
Gromov's alternative, contact shape, and C^0-rigidity of contact diffeomorphisms
Stefan Müller, Peter Spaeth
We prove that the group of contact diffeomorphisms is closed in the group of all diffeomorphisms in the C^0-topology. By Gromov's alternative, it suffices to exhibit a diffeomorphi…
Topological contact dynamics III: uniqueness of the topological Hamiltonian and C^0-rigidity of the geodesic flow
Stefan Müller, Peter Spaeth
We prove that a topological contact isotopy uniquely defines a topological contact Hamiltonian. Combined with previous results from [MS11], this generalizes the classical one-to-on…
Topological contact dynamics II: topological automorphisms, contact homeomorphisms, and non-smooth contact dynamical systems
Stefan Müller, Peter Spaeth
This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evid…
Topological contact dynamics I: symplectization and applications of the energy-capacity inequality
Stefan Müller, Peter Spaeth
We introduce topological contact dynamics of a smooth manifold carrying a cooriented contact structure, generalizing previous work in the case of a symplectic structure [MO07] or a…
On properly essential classical conformal diffeomorphism groups
Stefan Müller, Peter Spaeth
We prove that various classical conformal diffeomorphism groups, which are known to be essential [1], are in fact properly essential. This is a consequence of a local criterion on…
Helicity of vector fields preserving a regular contact form and topologically conjugate smooth dynamical systems
Stefan Müller, Peter Spaeth
We compute the helicity of a vector field preserving a regular contact form on a closed three-dimensional manifold, and improve results by J.-M. Gambaudo and É. Ghys [GG97] relatin…
Uniqueness of contact Hamiltonians of topological strictly contact isotopies
Augustin Banyaga, Peter Spaeth
We prove that for regular contact forms there exists a bijective correspondence between the limits of sequences of smooth strictly contact isotopies and the limits with respe…
Length minimizing paths in the Hamiltonian diffeomorphism group
Peter Spaeth
On any closed symplectic manifold we construct a path-connected neighborhood of the identity in the Hamiltonian diffeomorphism group with the property that each Hamiltonian diffeom…