164 research outputs found
Driven cofactor systems and Hamilton-Jacobi separability
This is a continuation of the work initiated in a previous paper on so-called
driven cofactor systems, which are partially decoupling second-order
differential equations of a special kind. The main purpose in that paper was to
obtain an intrinsic, geometrical characterization of such systems, and to
explain the basic underlying concepts in a brief note. In the present paper we
address the more intricate part of the theory. It involves in the first place
understanding all details of an algorithmic construction of quadratic integrals
and their involutivity. It secondly requires explaining the subtle way in which
suitably constructed canonical transformations reduce the Hamilton-Jacobi
problem of the (a priori time-dependent) driven part of the system into that of
an equivalent autonomous system of St\"ackel type
Many parameter Hoelder perturbation of unbounded operators
If is a -mapping, for , having
as values unbounded self-adjoint operators with compact resolvents and common
domain of definition, parametrized by in an (even infinite dimensional)
space, then any continuous (in ) arrangement of the eigenvalues of is
indeed in .Comment: LaTeX, 4 pages; The result is generalized from Lipschitz to Hoelder.
Title change
Climate intervention on a high-emissions pathway could delay but not prevent West Antarctic Ice Sheet demise
The Stratified Structure of Spaces of Smooth Orbifold Mappings
We consider four notions of maps between smooth C^r orbifolds O, P with O
compact (without boundary). We show that one of these notions is natural and
necessary in order to uniquely define the notion of orbibundle pullback. For
the notion of complete orbifold map, we show that the corresponding set of C^r
maps between O and P with the C^r topology carries the structure of a smooth
C^\infty Banach (r finite)/Frechet (r=infty) manifold. For the notion of
complete reduced orbifold map, the corresponding set of C^r maps between O and
P with the C^r topology carries the structure of a smooth C^\infty Banach (r
finite)/Frechet (r=infty) orbifold. The remaining two notions carry a
stratified structure: The C^r orbifold maps between O and P is locally a
stratified space with strata modeled on smooth C^\infty Banach (r
finite)/Frechet (r=infty) manifolds while the set of C^r reduced orbifold maps
between O and P locally has the structure of a stratified space with strata
modeled on smooth C^\infty Banach (r finite)/Frechet (r=infty) orbifolds.
Furthermore, we give the explicit relationship between these notions of
orbifold map. Applying our results to the special case of orbifold
diffeomorphism groups, we show they inherit the structure of C^\infty Banach (r
finite)/Frechet (r=infty) manifolds. In fact, for r finite they are topological
groups, and for r=infty they are convenient Frechet Lie groups.Comment: 31 pages, 2 figures; corrected and expande
Denjoy-Carleman differentiable perturbation of polynomials and unbounded operators
Let for be a -mapping with values unbounded
operators with compact resolvents and common domain of definition which are
self-adjoint or normal. Here stands for C^\om (real analytic), a
quasianalytic or non-quasianalytic Denjoy-Carleman class, , or a
H\"older continuity class C^{0,\al}. The parameter domain is either
or or an infinite dimensional convenient vector
space. We prove and review results on -dependence on of the
eigenvalues and eigenvectors of .Comment: 8 page
Flat bidifferential ideals and semihamiltonian PDEs
In this paper we consider a class of semihamiltonian systems characterized by
the existence of a special conservation law.
The density and the current of this conservation law satisfy a second order
system of PDEs which has a natural interpretation in the theory of flat
bifferential ideals. The class of systems we consider contains important
well-known examples of semihamiltonian systems. Other examples, like genus 1
Whitham modulation equations for KdV, are related to this class by a
reciprocal trasformation.Comment: 18 pages. v5: formula (36) corrected; minor change
Cohomological aspects on complex and symplectic manifolds
We discuss how quantitative cohomological informations could provide
qualitative properties on complex and symplectic manifolds. In particular we
focus on the Bott-Chern and the Aeppli cohomology groups in both cases, since
they represent useful tools in studying non K\"ahler geometry. We give an
overview on the comparisons among the dimensions of the cohomology groups that
can be defined and we show how we reach the -lemma
in complex geometry and the Hard-Lefschetz condition in symplectic geometry.
For more details we refer to [6] and [29].Comment: The present paper is a proceeding written on the occasion of the
"INdAM Meeting Complex and Symplectic Geometry" held in Cortona. It is going
to be published on the "Springer INdAM Series
Contrasting Impact of Future CO 2 Emission Scenarios on the Extent of CaCO 3 Mineral Undersaturation in the Humboldt Current System
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