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Related papers: Index computations in Rabinowitz Floer homology

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We define boundedness properties on the contractible fixed points set of the time-one map of an identity isotopy on a closed oriented surface with genus $g\geq1$. In symplectic geometry, a classical object is the notion of action function,…

Dynamical Systems · Mathematics 2012-09-11 Jian Wang

This paper is devoted to the analysis of a class of $F(R)$ gravity, where additional logarithmic corrections are assumed. The gravitational action includes an exponential term and a $R^2$ inflationary term, both with logarithmic…

General Relativity and Quantum Cosmology · Physics 2019-01-09 Sergei D. Odintsov , Diego Saez-Chillon Gomez , German S. Sharov

The purpose of this paper is to prove a new, more general version of the Morse index theorem for heteroclinic, homoclinic, and half-clinic solutions in general Lagrangian systems. In the final section, we compute the Morse index for…

Dynamical Systems · Mathematics 2025-12-17 Xijun Hu , Alessandro Portaluri , Li Wu , Qin Xing

Area-preserving diffeomorphisms of a 2-disc can be regarded as time-1 maps of (non-autonomous) Hamiltonian flows on solid tori, periodic flow-lines of which define braid (conjugacy) classes, up to full twists. We examine the dynamics…

Dynamical Systems · Mathematics 2009-10-06 J. -B. van den Berg , R. Ghrist , R. Vandervorst , W. Wojcik

Morse index theory provides an elegant and useful tool for describing several aspects of a Lagrangian system in terms of its variational properties. In the classical framework it provides an equality between the spectral properties of a…

Mathematical Physics · Physics 2023-05-30 Alessandro Portaluri , Li Wu , Ran Yang

In this paper we establish the existence of periodic orbits belonging to any $\sigma$-atoroidal free homotopy class for Hamiltonian systems in the twisted disc bundle, provided that the compactly supported time-dependent Hamiltonian…

Symplectic Geometry · Mathematics 2019-11-20 Wenmin Gong

This 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…

Symplectic Geometry · Mathematics 2020-06-18 Federica Pasquotto , Robert Vandervorst , Jagna Wiśniewska

This article is a tribute to the memory of Professor Enzo Martinelli, with deep respect and reconesance. Nicolae Teleman. The index formula is a local statement made on global and local data; for this reason we introduce local Alexander -…

K-Theory and Homology · Mathematics 2016-10-17 Nicolae Teleman

Coupled Maxwell and time-dependent orbital-free calculations are implemented and tested to describe the interaction of electromagnetic waves and matter. The currents and induced fields predicted by the orbital-free calculations are compared…

Mesoscale and Nanoscale Physics · Physics 2021-02-17 Cody Covington , Justin Malave , Kalman Varga

The aim of this paper is to give an explicit formula for the calculation of the Gutzwiller--Maslov index of a Hamiltonian periodic orbit. We identify the index appearing in Gutzwiller's trace formula with a non-trivial extension of the…

Mathematical Physics · Physics 2007-05-23 Maurice De Gosson , Serge De Gosson

In the setting of several commuting operators on a Hilbert space one defines the notions of invertibility and Fredholmness in terms of the associated Koszul complex. The index problem then consists of computing the Euler characteristic of…

K-Theory and Homology · Mathematics 2012-10-24 Jens Kaad , Ryszard Nest

Heteroclinic orbits for one-parameter families of nonautonomous vectorfields appear in a very natural way in many physical applications. Inspired by some recent bifurcation results for homoclinic trajectories of nonautonomous vectorfield,…

Dynamical Systems · Mathematics 2017-04-25 Xijun Hu , Alessandro Portaluri

Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…

Astrophysics · Physics 2011-10-05 Giuseppe Pucacco , Dino Boccaletti , Cinzia Belmonte

This is an expository paper devoted to the Morse index of Chaperon's generating families of Hamiltonian diffeomorphisms. After reviewing the construction of such generating families, we present Bott's iteration theory in this setting: we…

Symplectic Geometry · Mathematics 2016-11-22 Marco Mazzucchelli

Inspired by constructions of Kova\v{c}evi\'{c}, we introduce the amalgamated free product of circle actions, obtained by blowing up two actions along prescribed orbits and rearranging the inserted intervals. Under natural orbit and index…

Dynamical Systems · Mathematics 2026-04-28 João Carnevale

We define Floer homology for a time-independent, or autonomous Hamiltonian on a symplectic manifold with contact type boundary, under the assumption that its 1-periodic orbits are transversally nondegenerate. Our construction is based on…

Symplectic Geometry · Mathematics 2008-04-30 Frédéric Bourgeois , Alexandru Oancea

We prove the existence of infinitely many periodic points of symplectomorphisms isotopic to the identity if they admit at least one (non-contractible) hyperbolic periodic orbit and satisfy some condition on its flux. The obtained periodic…

Dynamical Systems · Mathematics 2015-08-27 Marta Batoréo

When a finite group freely acts on a topological space, we can define its index and coindex. They roughly measure the size of the given action. We explore the interaction between this index theory and topological dynamics. Given a…

Dynamical Systems · Mathematics 2021-03-24 Ruxi Shi , Masaki Tsukamoto

We present a natural orbital-based implementation of the intermediate Hamiltonian Fock space coupled-cluster method for (1,1) sector of Fock space. The use of natural orbital significantly reduces the computational cost and can…

Chemical Physics · Physics 2021-09-07 Soumi Haldar , Achintya Kumar Dutta

We consider a {\em Hamiltonian setup} $\sextuple$, where $(\mathcal M,\omega)$ is a symplectic manifold, $\mathfrak L$ is a distribution of Lagrangian subspaces in $\mathcal M$, $\mathcal P$ a Lagrangian submanifold of $ \mathcal M$, $H$ is…

Differential Geometry · Mathematics 2007-05-23 Paolo Piccione , Daniel Victor Tausk