Displaying similar documents to “A polynomial class of Markus-Yamabe counterexamples.”

A sufficient condition for a polynomial centre to be global

Marco Sabatini (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

A sufficient condition is given in order that a centre of a polynomial planar autonomous system be a global centre.

Quasi-homogeneous linear systems on ℙ² with base points of multiplicity 7, 8, 9, 10

Marcin Dumnicki (2011)

Annales Polonici Mathematici

Similarity:

We prove that the Segre-Gimigliano-Harbourne-Hirschowitz conjecture holds for quasi-homogeneous linear systems on ℙ² for m = 7, 8, 9, 10, i.e. systems of curves of a given degree passing through points in general position with multiplicities at least m,...,m,m₀, where m = 7, 8, 9, 10, m₀ is arbitrary.

Quasi-invariant subspaces generated by polynomials with nonzero leading terms

Kunyu Guo, Shengzhao Hou (2004)

Studia Mathematica

Similarity:

We introduce a partial order relation in the Fock space. Applying it we show that for the quasi-invariant subspace [p] generated by a polynomial p with nonzero leading term, a quasi-invariant subspace M is similar to [p] if and only if there exists a polynomial q with the same leading term as p such that M = [q].

Lyapunov quasi-stable trajectories

Changming Ding (2013)

Fundamenta Mathematicae

Similarity:

We introduce the notions of Lyapunov quasi-stability and Zhukovskiĭ quasi-stability of a trajectory in an impulsive semidynamical system defined in a metric space, which are counterparts of corresponding stabilities in the theory of dynamical systems. We initiate the study of fundamental properties of those quasi-stable trajectories, in particular, the structures of their positive limit sets. In fact, we prove that if a trajectory is asymptotically Lyapunov quasi-stable, then its limit...

Quasi-linear maps

D. J. Grubb (2008)

Fundamenta Mathematicae

Similarity:

A quasi-linear map from a continuous function space C(X) is one which is linear on each singly generated subalgebra. We show that the collection of quasi-linear functionals has a Banach space pre-dual with a natural order. We then investigate quasi-linear maps between two continuous function spaces, classifying them in terms of generalized image transformations.

A note on LaSalle's problems

Anna Cima, Armengol Gasull, Francesc Mañosas (2001)

Annales Polonici Mathematici

Similarity:

In LaSalle's book "The Stability of Dynamical Systems", the author gives four conditions which imply that the origin of a discrete dynamical system defined on ℝ is a global attractor, and proposes to study the natural extensions of these conditions in ℝⁿ. Although some partial results are obtained in previous papers, as far as we know, the problem is not completely settled. In this work we first study the four conditions and prove that just one of them implies that the origin is a global...