Arnold VJ - Academia.edu (original) (raw)
Address: Arequipa, Arequipa, Peru
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Papers by Arnold VJ
Mathematics of Computation, 1997
We study a class of permutation-symmetric globally-coupled, phase oscillator networks on N-dimens... more We study a class of permutation-symmetric globally-coupled, phase oscillator networks on N-dimensional tori. We focus on the efiects of symmetry and of the forms of the coupling functions, derived from un- derlying Hodgkin-Huxley type neuron models, on the existence, stability, and degeneracy of phase-locked solutions in which subgroups of oscillators share common phases. We also estimate domains of attraction for
International Immunology, 2005
This is the second part of an article in two parts, which builds the foundation of a Floer-theore... more This is the second part of an article in two parts, which builds the foundation of a Floer-theoretic invariant, I_F. (See math.DG/0111313 for part I). Having constructed I_F and outlined a proof of its invariance based on bifurcation analysis in part I, in this part we prove a series of gluing theorems to confirm the bifurcation behavior predicted in part I. These gluing theorems are different from (and much harder than) the more conventional versions in that they deal with broken trajectories or broken orbits connected at degenerate rest points. The issues of orientation and signs are also settled in the last section.
Transformation Groups, 2009
We prove complete integrability of the Manakov-type SO(n)-invariant geodesic flows on homogeneous... more We prove complete integrability of the Manakov-type SO(n)-invariant geodesic flows on homogeneous spaces SO(n)/SO(k1) ×⋯× SO(k r ), for any choice of k 1,…,k r , k 1 + ⋯ + k r ⩽ n. In particular, a new proof of the integrability of a Manakov symmetric rigid body motion around a fixed point is presented. Also, the proof of integrability of the SO(n)-invariant Einstein metrics on SO(k 1 + k 2 + k 3)/SO(k 1) × SO(k 2) × SO(k 3) and on the Stiefel manifolds V (n, k) = SO(n)/SO(k) is given.
In this article, we prove that there exists at least one chord which is characteristic of Reeb ve... more In this article, we prove that there exists at least one chord which is characteristic of Reeb vector field connecting a given Legendre submanifold in a closed contact manifold with any contact form.
Communications in Mathematical Physics, 2003
Let (M,g) be a C ∞ compact Riemann manifold with classical Hamiltonian, HC ∞ (T * M). Assume th... more Let (M,g) be a C ∞ compact Riemann manifold with classical Hamiltonian, HC ∞ (T * M). Assume that the corresponding -quantization P 1 :=Op (H) is quantum completely integrable. We establish an -microlocal Weyl law on short spectral intervals of size 2−ε;∀ε>0 for various families of operators P 1 u ;uI containing P 1 , both in the mean and pointwise a.e. for uI. The -microlocalization refers to a small tubular neighbourhood of a non-degenerate, stable periodic bicharacteristic γ⊂T * M−0.
Mathematics of Computation, 1997
We study a class of permutation-symmetric globally-coupled, phase oscillator networks on N-dimens... more We study a class of permutation-symmetric globally-coupled, phase oscillator networks on N-dimensional tori. We focus on the efiects of symmetry and of the forms of the coupling functions, derived from un- derlying Hodgkin-Huxley type neuron models, on the existence, stability, and degeneracy of phase-locked solutions in which subgroups of oscillators share common phases. We also estimate domains of attraction for
International Immunology, 2005
This is the second part of an article in two parts, which builds the foundation of a Floer-theore... more This is the second part of an article in two parts, which builds the foundation of a Floer-theoretic invariant, I_F. (See math.DG/0111313 for part I). Having constructed I_F and outlined a proof of its invariance based on bifurcation analysis in part I, in this part we prove a series of gluing theorems to confirm the bifurcation behavior predicted in part I. These gluing theorems are different from (and much harder than) the more conventional versions in that they deal with broken trajectories or broken orbits connected at degenerate rest points. The issues of orientation and signs are also settled in the last section.
Transformation Groups, 2009
We prove complete integrability of the Manakov-type SO(n)-invariant geodesic flows on homogeneous... more We prove complete integrability of the Manakov-type SO(n)-invariant geodesic flows on homogeneous spaces SO(n)/SO(k1) ×⋯× SO(k r ), for any choice of k 1,…,k r , k 1 + ⋯ + k r ⩽ n. In particular, a new proof of the integrability of a Manakov symmetric rigid body motion around a fixed point is presented. Also, the proof of integrability of the SO(n)-invariant Einstein metrics on SO(k 1 + k 2 + k 3)/SO(k 1) × SO(k 2) × SO(k 3) and on the Stiefel manifolds V (n, k) = SO(n)/SO(k) is given.
In this article, we prove that there exists at least one chord which is characteristic of Reeb ve... more In this article, we prove that there exists at least one chord which is characteristic of Reeb vector field connecting a given Legendre submanifold in a closed contact manifold with any contact form.
Communications in Mathematical Physics, 2003
Let (M,g) be a C ∞ compact Riemann manifold with classical Hamiltonian, HC ∞ (T * M). Assume th... more Let (M,g) be a C ∞ compact Riemann manifold with classical Hamiltonian, HC ∞ (T * M). Assume that the corresponding -quantization P 1 :=Op (H) is quantum completely integrable. We establish an -microlocal Weyl law on short spectral intervals of size 2−ε;∀ε>0 for various families of operators P 1 u ;uI containing P 1 , both in the mean and pointwise a.e. for uI. The -microlocalization refers to a small tubular neighbourhood of a non-degenerate, stable periodic bicharacteristic γ⊂T * M−0.