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Local dynamics of intersections: V. I. Arnold's theorem revisited  [PDF]
Anna Leah Seigal,Sergei Yakovenko
Mathematics , 2013, DOI: 10.1007/s11856-014-1065-4
Abstract: V. I. Arnold proved in 1991 (published in 1993) that the intersection multiplicity between two germs of analytic subvarieties at a fixed point of a holomorphic invertible self-map remains bounded when one of the germs is dragged by iterations of the self map. The proof is based on the Skolem-Mahler-Lech theorem on zeros in recurrent sequences. We give a different proof, based on the Noetherianity of certain algebras, which allows to generalize the Arnold's theorem for local actions of arbitrary finitely generated commutative groups, both with discrete and infinitesimal generators. Simple examples show that for non-commutative groups the analogous assertion fails.
Proofs On Arnold Conjectures  [PDF]
Renyi Ma
Mathematics , 2008,
Abstract: In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.
Il primato dell'istituzione in Arnold Gehlen  [cached]
Ubaldo Fadini
Scienza & Politica : per una Storia delle Dottrine , 1991, DOI: 10.6092/issn.1825-9618/3063
Abstract: Il primato dell'istituzione in Arnold Gehlen
Arnold Zweig, Bilanz der deutschen Judenheit, 1993  [cached]
Ulrich Wyrwa
Scienza & Politica : per una Storia delle Dottrine , 2000, DOI: 10.6092/issn.1825-9618/2868
Abstract: Arnold Zweig, Bilanz der deutschen Judenheit, 1993
Vladimir Igorevich Arnold  [PDF]
Oleg Karpenkov
Mathematics , 2010,
Abstract: In the following article a Ph.D. student of V.I.~Arnold gives a personal account on his teacher who unexpectedly passed away earlier this year.
Is Arnold diffusion relevant to global diffusion?  [PDF]
Seiichiro Honjo,Kunihiko Kaneko
Physics , 2003,
Abstract: Global diffusion of Hamiltonian dynamical systems is investigated by using a coupled standard maps. Arnold web is visualized in the frequency space, using local rotation numbers, while Arnold diffusion and resonance overlaps are distinguished by the residence time distributions at resonance layers. Global diffusion in the phase space is shown to be accelerated by diffusion across overlapped resonances generated by the coupling term, rather than Arnold diffusion along the lower-order resonances. The former plays roles of hubs for transport in the phase space, and accelerate the diffusion.
Introduction to Hydrodynamics  [PDF]
Sangyong Jeon,Ulrich Heinz
Physics , 2015,
Abstract: We give a pedagogical review of relativistic hydrodynamics relevant to relativistic heavy ion collisions. Topics discussed include linear response theory derivation of 2nd order viscous hydrodynamics including the Kubo formulas, kinetic theory derivation of 2nd order viscous hydrodynamics, anisotropic hydrodynamics and a brief review of numerical algorithms. Emphasis is given to the theory of hydrodynamics rather than phenomenology.
Adnan Burina,Dzevdet Smajlovic,Osman Sinanovic,Mirjana Vidovic
Acta Medica Saliniana , 2009, DOI: 10.5457/ams.31.09
Abstract: Generally, Arnold – Chiari malformation associated with syringomyelia is not rare. In this case report we present a 52 years old female patient with a history of neck-pain, low-back pain, pain in both arms as well as frequent numbness in the lateral regions of both arms. She also experienced walk disturbance and in her previous history she reports a car accident, twenty-eight years ago. She broke windshield with her forehead, but remained conscious at the time. At the time of admittance at the Department of Neurology, her neurological status was remarkable for cerebellar symptomatology (ataxia, positive Romberg-sign, finger–nose test which she did with tremor and was not able to perform tandem-walk ), hypoestesia of the right side of the body, hyper-reflection of both arms and legs, bilaterally, more pronounced at the right side; right foot subclonus and spastic-ataxic walk. Neurological status could not be explained by previously performed tests: x-ray of cervical spine, lumbal myelography, computerized tomography (CT) of the brain. However, magnetic resonance imaging (MRI) of the brain and cervical spine verified Arnold-Chiari malformation (type I) associated with syringomyelia from C3 to C7. Patient was referred to surgery and subsequent physical rehabilitation.
The speed of Arnold diffusion  [PDF]
Christos Efthymiopoulos,Mirella Harsoula
Physics , 2013, DOI: 10.1016/j.physd.2013.01.016
Abstract: A detailed numerical study is presented of the slow diffusion (Arnold diffusion) taking place around resonance crossings in nearly integrable Hamiltonian systems of three degrees of freedom in the so-called `Nekhoroshev regime'. The aim is to construct estimates regarding the speed of diffusion based on the numerical values of a truncated form of the so-called remainder of a normalized Hamiltonian function, and to compare them with the outcomes of direct numerical experiments using ensembles of orbits. In this comparison we examine, one by one, the main steps of the so-called analytic and geometric parts of the Nekhoroshev theorem. We are led to two main results: i) We construct in our concrete example a convenient set of variables, proposed first by Benettin and Gallavotti (1986), in which the phenomenon of Arnold diffusion in doubly resonant domains can be clearly visualized. ii) We determine, by numerical fitting of our data the dependence of the local diffusion coefficient "D" on the size "||R_{opt}||" of the optimal remainder function, and we compare this with a heuristic argument based on the assumption of normal diffusion. We find a power law "D\propto ||R_{opt}||^{2(1+b)}", where the constant "b" has a small positive value depending also on the multiplicity of the resonance considered.
On strict category weight and Arnold conjecture  [PDF]
Yuli B. Rudyak
Mathematics , 1998,
Abstract: In [R2] and [RO] the Arnold conjecture for closed symplectic manifolds with trivial second homotopy group was proved. This proof used surgery and cobordism theory. Here we give a purely cohomological proof of this result.
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