On local first order structural stability of pairings of vector fields and functions
On lopsided systems.
On Lyapunov stability in hypoplasticity
We investigate the Lyapunov stability implying asymptotic behavior of a nonlinear ODE system describing stress paths for a particular hypoplastic constitutive model of the Kolymbas type under proportional, arbitrarily large monotonic coaxial deformations. The attractive stress path is found analytically, and the asymptotic convergence to the attractor depending on the direction of proportional strain paths and material parameters of the model is proved rigorously with the help of a Lyapunov function....
On maximal transitive sets of generic diffeomorphisms
On maximizing measures of homeomorphisms on compact manifolds
We prove that given a compact n-dimensional connected Riemannian manifold X and a continuous function g: X → ℝ, there exists a dense subset of the space of homeomorphisms of X such that for all T in this subset, the integral , considered as a function on the space of all T-invariant Borel probability measures μ, attains its maximum on a measure supported on a periodic orbit.
On measure theoretical analogues of the Takesaki structure theorem for type III factors
The orbit equivalence of type ergodic equivalence relations is considered. We show that it is equivalent to the outer conjugacy problem for the natural trace-scaling action of a countable dense ℝ-subgroup by automorphisms of the Radon-Nikodym skew product extensions of these relations. A similar result holds for the weak equivalence of arbitrary type cocycles with values in Abelian groups.
On metric properties of substitutions
On minimal and invariant sets in semidynamical systems.
On minimal laminations of the torus
On minimal sets in 2-manifolds.
On miura transformations and Volterra-type equations associated with the adler-bobenko-suris equations.
On multiplicatively dependent linear numeration systems, and periodic points
Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers and respectively, such that and are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.
On multiplicatively dependent linear numeration systems, and periodic points
Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers β and γ respectively, such that β and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.
On natural invariant measures on generalised iterated function systems.
On negative escape time in semidynamical systems.
On new spectral multiplicities for ergodic maps
It is shown that each subset of positive integers that contains 2 is realizable as the set of essential values of the multiplicity function for the Koopman operator of some weakly mixing transformation.
On nonlinear equations integrable in theta-functions of nonprincipally polarized Abelian varieties.
On nonlinear Schrödinger equations
On nonlinear Schrödinger equations in exterior domains
On non-point invertible transformations of difference and differential-difference equations.