On rational and periodic solutions of stationary KdV equations.
On rational maps with two critical points.
On regular polynomial endomorphisms of ℂ2 without bounded critical orbitswithout bounded critical orbits
We study conditions involving the critical set of a regular polynomial endomorphism f∶ℂ2↦ℂ2 under which all complete external rays from infinity for f have well defined endpoints.
On Semicontinuity in Impulsive Dynamical Systems
In the important paper on impulsive systems [K1] several notions are introduced and several properties of these systems are shown. In particular, the function ϕ which describes "the time of reaching impulse points" is considered; this function has many important applications. In [K1] the continuity of this function is investigated. However, contrary to the theorem stated there, the function ϕ need not be continuous under the assumptions given in the theorem. Suitable examples are shown in this paper....
On Semi-Stability for Diffeomorphisms.
On simultaneous Abel equations.
On singularities of Hamiltonian mappings
The notion of an implicit Hamiltonian system-an isotropic mapping H: M → (TM,ω̇) into the tangent bundle endowed with the symplectic structure defined by canonical morphism between tangent and cotangent bundles of M-is studied. The corank one singularities of such systems are classified. Their transversality conditions in the 1-jet space of isotropic mappings are described and the corresponding symplectically invariant algebras of Hamiltonian generating functions are calculated.
On small stochastic perturbations of mappings of the unit interval
On solutions of functional equations determining subsemigroups of L¹₄
Let L¹₄ be the group of 4-jets at zero of diffeomorphisms f of ℝ with f(0) = 0. Identifying jets with sequences of derivatives, we determine all subsemigroups of L¹₄ consisting of quadruples (x₁,f(x₁,x₄),g(x₁,x₄),x₄) ∈ (ℝ∖{0}) × ℝ³ with continuous functions f,g:(ℝ∖{0}) × ℝ → ℝ. This amounts to solving a set of functional equations.
On solvability of the cohomology equation in function spaces
Let T be an endomorphism of a probability measure space (Ω,𝓐,μ), and f be a real-valued measurable function on Ω. We consider the cohomology equation f = h ∘ T - h. Conditions for the existence of real-valued measurable solutions h in some function spaces are deduced. The results obtained generalize and improve a recent result of Alonso, Hong and Obaya.
On some completions of the space of hamiltonian maps
In one of his papers, C. Viterbo defined a distance on the set of Hamiltonian diffeomorphisms of endowed with the standard symplectic form . We study the completions of this space for the topology induced by Viterbo’s distance and some others derived from it, we study their different inclusions and give some of their properties. In particular, we give a convergence criterion for these distances that allows us to prove that the completions contain non-ordinary elements, as for example, discontinuous...
On some dynamical properties of S-unimodal maps on an interval
On some integrable cases in surface theory
On some integral inequalities on time scales and their applications.
On some issues concerning polynomial cycles
We consider two issues concerning polynomial cycles. Namely, for a discrete valuation domain of positive characteristic (for ) or for any Dedekind domain of positive characteristic (but only for ), we give a closed formula for a set of all possible cycle-lengths for polynomial mappings in . Then we give a new property of sets , which refutes a kind of conjecture posed by W. Narkiewicz.
On some Markov matrices arising from the generalized Collatz mapping
On some notions of chaos in dimension zero
We compare four different notions of chaos in zero-dimensional systems (subshifts). We provide examples showing that in that case positive topological entropy does not imply strong chaos, strong chaos does not imply complicated dynamics at all, and ω-chaos does not imply Li-Yorke chaos.
On some properties of focal points.
On some properties of orientation-preserving surjections on the circle
On some properties of the Lüroth-type alternating series representations for real numbers.