Related papers: Bounded orbits of certain diagonalizable flows on …

We prove that subharmonic functions of finite order on finite dimensional real space, bounded from above outside of some asymptotically small sets on spheres, are bounded from above everywhere. It follows that subharmonic functions of…

In this paper we present a computer-assisted procedure for proving the existence of transverse heteroclinic orbits connecting hyperbolic equilibria of polynomial vector fields. The idea is to compute high-order Taylor approximations of…

We prove logarithm laws for unipotent flows on non-compact finite-volume hyperbolic manifolds. Our method depends on the estimate of norms of certain incomplete Eisenstein series.

A floating hemisphere under forced harmonic oscillation at very high and very low frequencies is considered. The problem is reduced to an elliptic one, that is, the Laplace operator in the exterior domain with standard Dirichlet and Neumann…

We consider a class of smooth mixing flows $T^{\alpha,\gamma}$ on $\mathbb{T}^2$ with one degenerated fixed point $x_0\in \mathbb{T}^2$ of power type $\gamma\in (-1,0)$. We prove that for a $G_\delta$ dense set of $\alpha\in \mathbb{T}$, a…

We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…

Orbital semilattices are introduced as bounded semilattices that are, in addition, equipped with an outer multiplication (a semigroup action) and diagonals (a concept borrowed from cylindric algebra), where each semilattice element has a…

We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…

Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…

We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…

In this paper we consider a semilinear parabolic equation in an infinite cylinder. The spatially varying nonlinearity is such that it connects two (spatially independent) bistable nonlinearities in a compact set in space. We prove that,…

It is proved that, if $(P_n)$ is a sequence of polynomials with complex coefficients having unbounded valences and tending to infinity at sufficiently many points, then there is an infinite dimensional closed subspace of entire functions,…

We study the distribution of non-discrete orbits of geometrically finite groups in $\operatorname{SO}(n,1)$ acting on $\mathbb{R}^{n+1}$, and more generally on the quotient of $\operatorname{SO}(n,1)$ by a horospherical subgroup. Using…

We prove Calegari's conjecture that every quasigeodesic flow on a closed hyperbolic 3-manifold has closed orbits.

For each $n\in\mathbb{Z}^+$, we show the existence of Venice masks (i.e. intransitive sectional-Anosov flows with dense periodic orbits) containing $n$ equilibria on certain compact 3-manifolds. These examples are characterized because of…

Subsets of a matrix algebra over a field that are invariant under conjugation and contain the linear span of each two of their commuting elements are described. They obviously include the subsets of diagonalizable and nilpotent matrices. In…

Let $M$ be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian $H:T^*M\rightarrow \mathbb R$ and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits…

We prove that the super-linearizability of polynomial systems is preserved by all currently known classes of polynomial automorphisms of $\R^n$. We then establish connections between such automorphisms and a sufficient condition for…

We consider the 3 by 3 determinant polynomial and we describe the limit points of the set of all polynomials obtained from the determinant polynomial by linear change of variables. This answers a question of J. M. Landsberg.

Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has nonzero linking number with this periodic…