43 citations · 120 across the 11 of their papers we have counts for
12 papers
Almost Existence From the Feral Perspective and Some Questions
Joel W. Fish, Helmut Hofer
This paper is concerned with the "almost existence" phenomenon for periodic orbits of Hamiltonian dynamical systems. In particular, we recover this result in both some standard and…
Feral Curves and Minimal Sets
Joel W. Fish, Helmut Hofer
Here we prove that for each Hamiltonian function defined on the standard symplectic , for which $M:=H^{-1}(…
Exhaustive Gromov compactness for pseudoholomorphic curves
Joel W. Fish, Helmut Hofer
Here we extend the notion of target-local Gromov convergence of pseudoholomorphic curves to the case in which the target manifold is not compact, but rather is exhausted by compact…
Lectures on Polyfolds and Symplectic Field Theory
Joel W. Fish, Helmut Hofer
This is a lecture note prepared for the SFT 9 workshop in Augsburg, Germany. The text describes a polyfold approach to the construction of symplectic field theory and focuses on th…
Polyfold and SFT Notes II: Local-Local M-Polyfold Constructions
Joel W. Fish, Helmut Hofer
Some early chapters of the upcoming book "Polyfold Constructions: Tools, Techniques, and Functors"
Polyfold and SFT Notes I: A Primer on Polyfolds and Construction Tools
Joel W. Fish, Helmut Hofer
Notes for the upcoming Workshop on Symplectic Field Theory IX, Polyfolds for SFT. These notes are essentially the first few chapters of a forthcoming book entitled "Polyfold Constr…
Connected sums and finite energy foliations I: Contact connected sums
Joel W. Fish, Richard Siefring
We consider a -manifold equipped with nondegenerate contact form and compatible almost complex structure . We show that if the data admits a stable finite…
Polyfolds: A First and Second Look
Oliver Fabert, Joel W. Fish, Roman Golovko +1
Polyfold theory was developed by Hofer-Wysocki-Zehnder by finding commonalities in the analytic framework for a variety of geometric elliptic PDEs, in particular moduli spaces of p…
The Conley-Zehnder indices of the rotating Kepler problem
Peter Albers, Joel W. Fish, Urs Frauenfelder +1
We determine the Conley-Zehnder indices of all periodic orbits of the rotating Kepler problem for energies below the critical Jacobi energy. Consequently, we show the universal cov…
Global surfaces of section in the planar restricted 3-body problem
Peter Albers, Joel W. Fish, Urs Frauenfelder +2
The restricted planar three-body problem has a rich history, yet many unanswered questions still remain. In the present paper we prove the existence of a global surface of section…
Estimates for J-curves as submanifolds
Joel W. Fish
Here we develop some basic analytic tools to study compactness properties of -curves (i.e. pseudo-holomorphic curves) when regarded as submanifolds. Incorporating techniques fro…
Target-local Gromov compactness
Joel W. Fish
We prove a version of Gromov's compactness theorem for pseudo-holomorphic curves which holds locally in the target symplectic manifold. This result applies to sequences of curves w…