4,908 research outputs found
Generic properties of the Rabinowitz unbounded continuum
No full textIn this article, we prove that, generically in the sense of domain variations, any solution to a nonlinear eigenvalue problem is either nondegenerate or the Crandall-Rabinowitz transversality condition that is satisfied. We then deduce that, generically, the unbounded Rabinowitz continuum of solutions is a simple analytic curve. The global bifurcation diagram resembles the classic model case of the Gel’fand problem in two dimensions
Generic properties of the Rabinowitz unbounded continuum
No full textIn this article, we prove that, generically in the sense of domain variations, any solution to a nonlinear eigenvalue problem is either nondegenerate or the Crandall-Rabinowitz transversality condition that is satisfied. We then deduce that, generically, the unbounded Rabinowitz continuum of solutions is a simple analytic curve. The global bifurcation diagram resembles the classic model case of the Gel'fand problem in two dimensions
Rabinowitz Floer homology and coisotropic intersections
No full text학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2014. 2. Urs Frauenfelder.Urs Frauenfelder와 Kai Cieliebak은 Paul Rabinowitz가 자율적 해밀턴 시스템에서 주기궤도들 찾기 위해 제안한 라그랑즈 승수 함수를 사용하여 Rabinowitz Floer homology 이론을 개발하였다.
이 논문에서는 우리는 임의의 여차원을 가지는 여등방성 부분다양체 위의 역학구조를 분석하는데 적합한 여러개의 Lagrange 상수들을 가지는 일반화된 Rabinowitz 함수를 연구할 것이다. 우리는 일반화된 Rabinowitz 함수를 사용하여 여등방성 궤적 교차점, 여등방성 부분 다양체의 전치가능성, 그리고 여등방성 부분다양체의 Rabinowitz Floer homology 등에 관해 연구할 것이다. 우리는 또한 Rabinowitz Floer homology의 Künneth 공식을 유도하여 무한개의 여등방 궤적 교차점을 가지는 여등방성 부분다양체들을 찾을 것이다. 이 연구는 여러 개의 운동 상수 (보존량) 를 가지는 운동 시스템을 연구하는데 중요한 역할을 할 것이다.Rabinowitz Floer homology theory was developed by Kai Cieliebak and Urs Frauenfelder using a Lagrange multiplier action functional, which was introduced by Paul Rabinowitz in order to detect periodic orbits of autonomous Hamiltonian systems.
In this thesis, we study a generalized Rabinowitz action functional with several Lagrange multipliers, which is well suited for exploring dynamics on coisotropic submanifolds of arbitrary codimensions. Using this, we investigate among others, the existence problem of leafwise coisotropic intersection points, displaceability of coisotropic submanifolds, and Rabinowitz Floer homology for coisotropic submanifolds. We also derive a Künneth formula for the Rabinowitz Floer homology of product coisotropic submanifolds, and this enables us to find a class of coisotropic submanifolds which have infinitely many leafwise coisotropic intersection points. This study will serve as a crucial tool for exploring autonomous dynamical systems with several integrals.Abstract i
1 Preliminaries on symplectic geometry 1
1.1 Hamiltonian dieomorphisms 2
1.2 Coisotropic submanifolds 3
1.3 Examples of contact coisotropic submanifolds 9
2 Statement of the results 14
2.1 Assumptions on manifolds 15
2.2 Main theorem 17
2.3 Leafwise coisotropic intersections 18
2.4 Leafwise displacement energy 22
2.5 Rabinowitz Floer homology 23
2.6 Künneth formula 25
2.7 List of related results 27
3 The Rabinowitz action functional with several Lagrange multipliers 28
3.1 The Rabinowitz action functional for coisotropic submanifolds 28
3.2 The perturbed Rabinowitz action functional 30
3.2.1 Compactness 34
3.3 Proof of Theorem A 42
4 The existence of a periodic orbit and the leafwise displacement energy 49
4.1 Proof of Theorem D 50
5 Rabinowitz Floer homology 53
5.1 Boundary Operator 54
5.2 Continuation Homomorphism 58
5.3 Proof of Theorem E 60
5.4 Filtered Rabinowitz Floer Homology 61
5.5 Proof of Theorem B 62
5.6 Proof of Theorem C 65
6 Künneth formula in Rabinowitz Floer homology 69
6.1 Rabinowitz action functional for product manifolds 69
6.1.1 Compactness 71
6.2 Proof of Theorem F 74
6.3 Proof of Theorem G 78
7 Infinitely many leafwise intersection points 83
7.1 Proofs of Corollary F and Corollary G 83
Abstract (in Korean) 95
Acknowledgement (in Korean) 97Docto
Rabinowitz Floer homology for tentacular Hamiltonians
No full textThis paper extends the definition of Rabinowitz Floer homology to non-compact hypersurfaces. We present a general framework for the construction of Rabinowitz Floer homology in the non-compact setting under suitable compactness assumptions on the periodic orbits and the moduli spaces of Floer trajectories. We introduce a class of hypersurfaces arising as the level sets of specific Hamiltonians: strongly tentacular Hamiltonians for which the compactness conditions are satisfied, cf. [ 21], thus enabling us to define the Rabinowitz Floer homology for this class. Rabinowitz Floer homology in turn serves as a tool to address the Weinstein conjecture and establish existence of closed characteristics for non-compact contact manifolds
Highly quasilinear problems without the Ambrosetti-Rabinowitz condition
No full textWe show the existence of nontrivial solutions for a class of highly quasilinear problems in which the governing operators depend on the unknown function. By using a suitable variational setting and a weak version of the Cerami--Palais--Smale condition, we establish the desired result without assuming that the nonlinear source satisfies the Ambrosetti--Rabinowitz condition
First Steps in Twisted Rabinowitz-Floer Homology
No full textRabinowitz-Floer homology is the Morse-Bott homology in the sense of Floer
associated with the Rabinowitz action functional introduced by Kai Cieliebak
and Urs Frauenfelder in 2009. In our work, we consider a generalisation of this
theory to a Rabinowitz-Floer homology of a Liouville automorphism. As an
application, we show the existence of noncontractible periodic Reeb orbits on
quotients of symmetric star-shaped hypersurfaces. In particular, our theory
applies to lens spaces.Comment: 40 pages, 5 figures. Fixed typos and exposition. Improved main result
to hold for all even-dimensional lens spaces. Submitted to the Journal of
Symplectic Geometr
George Rabinowitz
No full textThe political science discipline lost one of its sharpest intellects and many of us lost a cherished dear friend when George Rabinowitz passed away, on March 18, 2011. George's death was entirely unexpected. He suffered a sudden cardiac arrest in Trondheim, Norway, where he was on leave from the University of North Carolina, Chapel Hill with a research fellowship.</jats:p
Lectures on Twisted Rabinowitz-Floer Homology
No full textRabinowitz-Floer homology is the Morse-Bott homology in the sense of Floer
associated with the Rabinowitz action functional introduced by Kai Cieliebak
and Urs Frauenfelder in 2009. In this manuscript, we consider a generalisation
of this theory to a Rabinowitz-Floer homology of a Liouville automorphism. As
an application, we show the existence of noncontractible periodic Reeb orbits
on quotients of symmetric star-shaped hypersurfaces. In particular, this theory
applies to lens spaces. Moreover, we prove a forcing theorem, which guarantees
the existence of a contractible twisted closed characteristic on a displaceable
twisted stable hypersurface in a symplectically aspherical geometrically
bounded symplectic manifold if there exists a contractible twisted closed
characteristic belonging to a Morse-Bott component, with energy difference
smaller or equal to the displacement energy of the displaceable hypersurface.Comment: 95 pages, 14 figures. arXiv admin note: text overlap with
arXiv:2105.1393
Folder 23 -- Rabinowitz, Sarah, Rabinowitz, Moses & Rabinowitz, Boris -- 1929 - 1932
No full textThe grandmother of Sarah, Moses, and Boris Rabinowitz brought the children to Juarez, Chihuahua, Mexico from Russia in 1924. She abandoned them a few years later and went to Canada.
This document is very long and contains many, many letters most of which deal with trying to get the children to Canada to be with their grandmother. There are complications; the grandmother entered Canada illegally, the boys are young and don\u27t have passports, and appear to be troublemakers. The U.S. won\u27t allow the boys to enter and Canada won\u27t allow entry without Mexican passports which they can\u27t get.
The grandmother and Sarah end up returning to Russia
Rabinowitz Floer homology as a Tate vector space
No full textWe show that the category of linearly topologized vector spaces over discrete fields constitutes the correct framework for algebraic structures on Floer homologies with field coefficients. Our case in point is the Poincaré duality theorem for Rabinowitz Floer homology. We prove that Rabinowitz Floer homology is a locally linearly compact vector space in the sense of Lefschetz, or, equivalently, a Tate vector space in the sense of Beilinson-Feigin-Mazur. Poincaré duality and the graded Frobenius algebra structure on Rabinowitz Floer homology then hold in the topological sense. Along the way, we develop in a largely self-contained manner the theory of linearly topologized vector spaces, with special emphasis on duality and completed tensor products, complementing results of Beilinson-Drinfeld, Beilinson, Rojas, Positselski, and Esposito-Penkov.57 page
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