On the unique continuation property for a nonlinear dispersive system.
The uniqueness theorem for the ergodic maximal operator is proved in the continous case.
It is shown that if two functions share the same uncentered (two-sided) ergodic maximal function, then they are equal almost everywhere.
Unlike in the invertible setting, Anosov endomorphisms may have infinitely many unstable directions. Here we prove, under the transitivity assumption, that an Anosov endomorphism of a closed manifold M is either special (that is, every x ∈ M has only one unstable direction), or for a typical point in M there are infinitely many unstable directions. Another result is the semi-rigidity of the unstable Lyapunov exponent of a codimension one Anosov endomorphism that is C¹-close to a linear endomorphism...
A matrix in -algebra (fuzzy matrix) is called weakly robust if is an eigenvector of only if is an eigenvector of . The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an algorithm for checking the weak robustness is described.
We study the zero-temperature limit for Gibbs measures associated to Frenkel–Kontorova models on . We prove that equilibrium states concentrate on configurations of minimal energy, and, in addition, must satisfy a variational principle involving metric entropy and Lyapunov exponents, a bit like in the Ruelle–Pesin inequality. Then we transpose the result to certain continuous-time stationary stochastic processes associated to the viscous Hamilton–Jacobi equation. As the viscosity vanishes, the...
In the present paper we prove the “zero-two” law for positive contractions in the Banach-Kantorovich lattices , constructed by a measure with values in the ring of all measurable functions.
For a continuous map f on a compact metric space (X,d), a set D ⊂ X is internally chain transitive if for every x,y ∈ D and every δ > 0 there is a sequence of points ⟨x = x₀,x₁,...,xₙ = y⟩ such that for 0 ≤ i< n. In this paper, we prove that for tent maps with periodic critical point, every closed, internally chain transitive set is necessarily an ω-limit set. Furthermore, we show that there are at least countably many tent maps with non-recurrent critical point for which there is a closed,...
We prove that for a given impulsive dynamical system there exists an isomorphism of the basic dynamical system such that in the new system equipped with the same impulse function each impulsive trajectory is global, i.e. the resulting dynamics is defined for all positive times. We also prove that for a given impulsive system it is possible to change the topology in the phase space so that we may consider the system as a semidynamical system (without impulses).
We study the group Aut(ℱ) of (self) isomorphisms of a holomorphic foliation ℱ with singularities on a complex manifold. We prove, for instance, that for a polynomial foliation on ℂ² this group consists of algebraic elements provided that the line at infinity ℂP(2)∖ℂ² is not invariant under the foliation. If in addition ℱ is of general type (cf. [20]) then Aut(ℱ) is finite. For a foliation with hyperbolic singularities at infinity, if there is a transcendental automorphism then the foliation is either...
Two different models for a Hopf-von Neumann algebra of bounded functions on the quantum semigroup of all (quantum) permutations of infinitely many elements are proposed, one based on projective limits of enveloping von Neumann algebras related to finite quantum permutation groups, and the second on a universal property with respect to infinite magic unitaries.