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Stability of foliations induced by rational maps

F. Cukierman, J. V. Pereira, I. Vainsencher (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space q ( r , d ) of singular foliations of codimension q and degree d on the complex projective space r , when 1 q r - 2 . We study the geometry of these irreducible components. In particular we prove that they are all rational varieties and we compute their projective degrees in several cases.

Stability of higher order singular points of Poisson manifolds and Lie algebroids

Jean-Paul Dufour, Aïssa Wade (2006)

Annales de l’institut Fourier

We study the stability of singular points for smooth Poisson structures as well as general Lie algebroids. We give sufficient conditions for stability lying on the first-order approximation (not necessarily linear) of a given Poisson structure or Lie algebroid at a singular point. The main tools used here are the classical Lichnerowicz-Poisson cohomology and the deformation cohomology for Lie algebroids recently introduced by Crainic and Moerdijk. We also provide several examples of stable singular...

Stability of Markov processes nonhomogeneous in time

Marta Tyran-Kamińska (1999)

Annales Polonici Mathematici

We study the asymptotic behaviour of discrete time processes which are products of time dependent transformations defined on a complete metric space. Our sufficient condition is applied to products of Markov operators corresponding to stochastically perturbed dynamical systems and fractals.

Stability of periodic waves in Hamiltonian PDEs

Sylvie Benzoni-Gavage, Pascal Noble, L. Miguel Rodrigues (2013)

Journées Équations aux dérivées partielles

Partial differential equations endowed with a Hamiltonian structure, like the Korteweg–de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for these waves is still in its infancy though. The issue has been tackled by various means. Of course, it is always possible to address stability from the spectral point of view. However, the link with nonlinear stability  - in fact, orbital stability, since we are...

Stability of unique pseudo almost periodic solutions with measure

Boulbaba Ghanmi, Mohsen Miraoui (2020)

Applications of Mathematics

By means of the fixed-point methods and the properties of the μ -pseudo almost periodic functions, we prove the existence, uniqueness, and exponential stability of the μ -pseudo almost periodic solutions for some models of recurrent neural networks with mixed delays and time-varying coefficients, where μ is a positive measure. A numerical example is given to illustrate our main results.

Stability of vibrations for some Kirchhoff equation with dissipation

Prasanta Kumar Nandi, Ganesh Chandra Gorain, Samarjit Kar (2014)

Applications of Mathematics

In this paper we consider the boundary value problem of some nonlinear Kirchhoff-type equation with dissipation. We also estimate the total energy of the system over any time interval [ 0 , T ] with a tolerance level γ . The amplitude of such vibrations is bounded subject to some restrictions on the uncertain disturbing force f . After constructing suitable Lyapunov functional, uniform decay of solutions is established by means of an exponential energy decay estimate when the uncertain disturbances are insignificant....

Stabilization of monomial maps in higher codimension

Jan-Li Lin, Elizabeth Wulcan (2014)

Annales de l’institut Fourier

A monomial self-map f on a complex toric variety is said to be k -stable if the action induced on the 2 k -cohomology is compatible with iteration. We show that under suitable conditions on the eigenvalues of the matrix of exponents of f , we can find a toric model with at worst quotient singularities where f is k -stable. If f is replaced by an iterate one can find a k -stable model as soon as the dynamical degrees λ k of f satisfy λ k 2 > λ k - 1 λ k + 1 . On the other hand, we give examples of monomial maps f , where this condition...

Stable ergodicity and julienne quasi-conformality

Charles Pugh, Michael Shub (2000)

Journal of the European Mathematical Society

In this paper we dramatically expand the domain of known stably ergodic, partially hyperbolic dynamical systems. For example, all partially hyperbolic affine diffeomorphisms of compact homogeneous spaces which have the accessibility property are stably ergodic. Our main tools are the new concepts – julienne density point and julienne quasi-conformality of the stable and unstable holonomy maps. Julienne quasi-conformal holonomy maps preserve all julienne density points.

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