Search Results - "Fish, Joel W"
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1
Global Surfaces of Section in the Planar Restricted 3-Body Problem
Published in Archive for rational mechanics and analysis (01-04-2012)“…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…”
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Almost Existence From the Feral Perspective and Some Questions
Published 29-06-2020“…This paper is concerned with the "almost existence" phenomenon for periodic orbits of Hamiltonian dynamical systems. In particular, we recover this result in…”
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Feral Curves and Minimal Sets
Published 16-12-2018“…Here we prove that for each Hamiltonian function $H\in \mathcal{C}^\infty(\mathbb{R}^4, \mathbb{R})$ defined on the standard symplectic $(\mathbb{R}^4,…”
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Exhaustive Gromov compactness for pseudoholomorphic curves
Published 22-11-2018“…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…”
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Lectures on Polyfolds and Symplectic Field Theory
Published 21-08-2018“…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…”
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Polyfold and SFT Notes II: Local-Local M-Polyfold Constructions
Published 14-08-2018“…Some early chapters of the upcoming book "Polyfold Constructions: Tools, Techniques, and Functors"…”
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Polyfold and SFT Notes I: A Primer on Polyfolds and Construction Tools
Published 18-06-2018“…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…”
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Connected sums and finite energy foliations I: Contact connected sums
Published 17-11-2013“…Journal of Symplectic Geometry, 16(6):1639-1748, 2018 We consider a $3$-manifold $M$ equipped with nondegenerate contact form $\lambda$ and compatible almost…”
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Polyfolds: A First and Second Look
Published 07-10-2016“…EMS Surv. Math. Sci. 3 (2016), 131-208 Polyfold theory was developed by Hofer-Wysocki-Zehnder by finding commonalities in the analytic framework for a variety…”
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Compactness results for pseudo-holomorphic curves
Published 01-01-2007“…Since their introduction by Gromov in 1985, pseudo-holomorphic curves have played an essential role in the study of symplectic topology. Also of substantial…”
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Dissertation -
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Target-local Gromov compactness
Published 05-05-2010“…Geom. Topol. 15 (2011) 765-826 We prove a version of Gromov's compactness theorem for pseudo-holomorphic curves which holds locally in the target symplectic…”
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12
Estimates for J-curves as submanifolds
Published 22-12-2009“…Here we develop some basic analytic tools to study compactness properties of $J$-curves (i.e. pseudo-holomorphic curves) when regarded as submanifolds…”
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Compactness results for pseudo-holomorphic curves
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Dissertation -
14
The Conley-Zehnder indices of the rotating Kepler problem
Published 10-01-2012“…Mathematical Proceedings of the Cambridge Philosophical Society, (2013), 243 - 260 We determine the Conley-Zehnder indices of all periodic orbits of the…”
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15
Global surfaces of section in the planar restricted 3-body problem
Published 20-03-2011“…Archive for Rational Mechanics and Analysis, (2012), 273-284 The restricted planar three-body problem has a rich history, yet many unanswered questions still…”
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Journal Article