On the Time Evolution of Statistical States for Anosov Systems.
On the topological charge conservation in the three-dimensional -model.
A field of three-component unit vectors on the dimensional spacetime is considered. Two field configurations with different values of the topological charge cannot be connected by the path of field configurations with a finite Euclidean action. Therefore there is no transition between them. The initial and final configurations are assumed to be continuous at infinity. The asymptotic behaviour of intermediate configurations may be arbitrary. The proof is based on the properties of the degree of...
On the topological dynamics and phase-locking renormalization of Lorenz-like maps
The aim of this paper is twofold. First we give a characterization of the set of kneading invariants for the class of Lorenz–like maps considered as a map of the circle of degree one with one discontinuity. In a second step we will consider the subclass of the Lorenz– like maps generated by the class of Lorenz maps in the interval. For this class of maps we give a characterization of the set of renormalizable maps with rotation interval degenerate to a rational number, that is, of phase–locking...
On the topological equivalence between Anosov flows on the three-manifolds.
On the topology of an integrable variant of a nonholonomic Suslov problem
On the topology of solenoidal attractors of the cylinder
On the transitive and -limit points of the continuous mappings of the circle
We extend the recent results from the class of continuous maps of the interval to the class of continuous maps of the circle. Among others, we give a characterization of -limit sets and give a characterization of sets of transitive points for these maps.
On the transversal distribution and the complete figure in the second order multiple integral problem in the calculus of variations.
On the unique continuation property for a nonlinear dispersive system.
On the uniqueness of equilibrium states for piecewise monotone mappings
On the uniqueness of maximal operators for ergodic flows.
The uniqueness theorem for the ergodic maximal operator is proved in the continous case.
On the uniqueness of the fixed point index on differentiable manifolds.
On the uniqueness of the uncentered ergodic maximal function
It is shown that if two functions share the same uncentered (two-sided) ergodic maximal function, then they are equal almost everywhere.
On the unstable directions and Lyapunov exponents of Anosov endomorphisms
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...
On the Variation in the Cohomology of the Symplectic Form of the Reduced Phase Space.
On the Virasoro structure of symmetry algebras of nonlinear partial differential equations.
On the weak robustness of fuzzy matrices
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.
On the well posedness and refined estimates for the global attractor of the TYC model.
On the zero-temperature or vanishing viscosity limit for certain Markov processes arising from Lagrangian dynamics
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...
On the “zero-two” law for positive contractions in the Banach-Kantorovich lattice
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.