Construction of invariant sets for Anosov diffeomorphisms and hyperbolic attractors
Construction of non-constant and ergodic cocycles
We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on the "closure...
Contact geometry and complex surfaces.
Contact hamiltonians distinguishing locally certain Goursat systems
For the first time in dimension 9, the Goursat distributions are not locally smoothly classified by their small growth vector at a point. As shown in [M1], in dimension 9 of the underlying manifold 93 different local behaviours are possible and four irregular pairs of them have coinciding small growth vectors. In the present paper we distinguish geometrically objects in three of those pairs. Smooth functions in three variables - contact hamiltonians in the terminology of Arnold, [A] - help to do...
Contact integrable extensions and differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation
The method of contact integrable extensions is used to find new differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation and corresponding Bäcklund transformations.
Continuation of relative periodic orbits in a class of triatomic hamiltonian systems
Continuation of the connection matrix for singularly perturbed hyperbolic equations
Continued fractions and the Gauss map.
Continuity of attractors
Continuity of the Hausdorff dimension for invariant subsets of interval maps.
Continuity of the maps and .
Continuous and discrete (classical) Heisenberg spin chain revised.
Continuous and inverse shadowing for flows.
Continuous dependence of attractors on the shape of domain
Continuous dynamical systems on Taut complex manifolds
Continuous subadditive processes and formulae for Lyapunov characteristic exponents
Asymptotic properties of various semidynamical systems can be examined by means of continuous subadditive processes. To investigate such processes we consider different types of exponents: characteristic, central, singular and global exponents and we study their properties. We derive formulae for central and singular exponents and show that they provide upper bounds for characteristic exponents. The concept of conjugate processes introduced in this paper allows us to find lower bounds for characteristic...
Continuum many tent map inverse limits with homeomorphic postcritical ω-limit sets
We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical ω-limit set has cardinality of the continuum. The set of folding points (i.e. points at which the space is not homeomorphic to the product of a zero-dimensional set and an arc) of each of these spaces is also a Cantor set.
Continuum-wise expansive diffeomorphisms.
In this paper, we show that the C1 interior of the set of all continuum-wise expansive diffeomorphisms of a closed manifold coincides with the C1 interior of the set of all expansive diffeomorphisms. And the C1 interior of the set of all continuum-wise fully expansive diffeomorphisms on a surface is investigated. Furthermore, we have necessary and sufficient conditions for a diffeomorphism belonging to these open sets to be Anosov.
Contracting rigid germs in higher dimensions
Following Favre, we define a holomorphic germ to be rigid if the union of the critical set of all iterates has simple normal crossing singularities. We give a partial classification of contracting rigid germs in arbitrary dimensions up to holomorphic conjugacy. Interestingly enough, we find new resonance phenomena involving the differential of and its linear action on the fundamental group of the complement of the critical set.
Contracting singular cycles