On the ergodicity of the Weyl sums cocycle
On the estimation of averages over infinite intervals with an application to average persistence in population models.
On the existence and non-existence of closed trajectories for some Hamiltonian flows.
On the existence and stability of unfoldings of equivariant two-parameter bifurcation problems.
On the existence of a periodic solution of a nonlinear ordinary differential equation.
On the existence of an invariant measure for the dynamical system generated by partial differential equation
On the existence of bright solitons in cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity.
On the existence of chaotic behaviour of diffeomorphisms
For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt.
On the existence of cohomologous continuous cocycles for cocycles with values in some Lie groups
On the existence of equations of evolution.
On the existence of escaping geodesics.
On the existence of homoclinic points
On the existence of homoclinic solutions for almost periodic second order systems
On the existence of Hopf bifurcation in an open economy model
On the Exponential Bound of the Cutoff Resolvent
A simpler proof of a result of Burq [1] is presented.
On the finite blocking property
A planar polygonal billiard is said to have the finite blocking property if for every pair of points in there exists a finite number of “blocking” points such that every billiard trajectory from to meets one of the ’s. Generalizing our construction of a counter-example to a theorem of Hiemer and Snurnikov, we show that the only regular polygons that have the finite blocking property are the square, the equilateral triangle and the hexagon. Then we extend this result to translation surfaces....
On the forcing relation for surface homeomorphisms
On the formal first cocycle equation for iteration groups of type II
Let x be an indeterminate over ℂ. We investigate solutions αn : ℂ → ℂ, n ≥ 0, of the first cocycle equation in ℂ [[x]], the ring of formal power series over ℂ, where (F(s,x))s ∈ ℂ is an iteration group of type II, i.e. it is a solution of the translation equation of the form F(s,x) ≡ x + ck(s)xk mod xk+1, where k ≥ 2 and ck ≠ 0 is necessarily an additive function. It is easy to prove that the coefficient functions αn(s) of are polynomials in ck(s).It is possible to replace...
On the fractality of the biological tree-like structures.
On the -entropy and its Hudetz correction
The Hudetz correction of the fuzzy entropy is applied to the -entropy. The new invariant is expressed by the Hudetz correction of fuzzy entropy.