Related papers: Ergodic Homoclinic Groups, Infinite Sidon Construc…
For an integrable hierarchy which possesses a bihamiltonian structure with semisimple hydrodynamic limit, we prove that the linear reciprocal transformation with respect to any of its symmetry transforms it to another bihamiltonian…
We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any…
We continue our investigation of the nonlinear SUSY for complex potentials started in the Part I (math-ph/0610024) and prove the theorems characterizing its structure in the case of non-diagonalizable Hamiltonians. This part provides the…
We consider suspension flows built over interval exchange transformations with the help of roof functions having an asymmetric logarithmic singularity. We prove that such flows are strongly mixing for a full measure set of interval exchange…
In this paper, we study the ergodicity of a one-parameter diagonalizable subgroup of a connected semisimple real algebraic group $G$ acting on a homogeneous space or, more generally, a homogeneous-like space, equipped with a…
For a weakly mixing bounded rank-one construction the disjointness of its powers is proved. For non-rigid constructions we get minimal self-joinings. Examples of non-mixing rank one actions with explicit weak closure are proposed.
The symmetric top is a special case of the general top, and canonical Poisson structure on $T^*SE(3)$ is the common method of its description. This structure is invariant under the right action of $SO(3)$, but the Hamiltonian of the…
In connection with the results of Tim Austin, and Wen Huang, Song Shao, Xiangdong Ye we present the following assertion: there are infinite automorphisms $S,T$, some set $A$ of positive finite measure and a sequence $N_m$ with…
We prove a Simons-type holonomy theorem for totally skew 1-forms with values in a Lie algebra of linear isometries. The only transitive case, for this theorem, is the full orthogonal group. We only use geometric methods and we do not use…
We give a review of results on superpolynomial decay of correlations, and polynomial decay of correlations for nonuniformly expanding semiflows and nonuniformly hyperbolic flows. A self-contained proof is given for semiflows. Results for…
We prove that, for nice classes of infinite-dimensional smooth groups G, natural constructions in smooth topology and symplectic topology yield homotopically coherent group actions of G. This yields a bridge between infinite-dimensional…
Chung and Jiang showed that, if a one ended group contains an infinite order element, then every continuous cocycle over the full shift on that group, taking values in a discrete group, must be cohomologous to a homomorphism. We show that…
A continuous family of pairwise disjoint even factors of Gaussian suspensions for Sidon transformations is presented. These factors have the same Lebesgue spectrum, but different Kirillov-Kushnirenko entropy.
We give a combinatorial description (including explicit differential-form bases) for the cohomology groups of the space of n distinct nonzero complex numbers, with coefficients in rank-one local systems which are of finite monodromy around…
We consider the question of continuity of limit sets for sequences of geometrically finite subgroups of isometry groups of rank-one symmetric spaces, and prove analogues of classical (Kleinian) theorems in this context. In particular we…
In this paper a new supersymmetric extension of conformal mechanics is put forward. The beauty of this extension is that all variables have a clear geometrical meaning and the super-Hamiltonian turns out to be the Lie-derivative of the…
Following Part~I, we consider a class of reversible systems and study bifurcations of homoclinic orbits to hyperbolic saddle equilibria. Here we concentrate on the case in which homoclinic orbits are symmetric, so that only one control…
We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite…
A family of deformed models of the sine-Gordon-type can be generated by twisting the sine-Gordon model. As a particular case, the 3-sine-Gordon model is here addressed, whose differential configurational entropy and the differential…
The ergodic properties of two uncoupled oscillators, a horizontal and vertical one, residing in a class of non rectangular star-shaped polygons with only vertical and horizontal boundaries and impacting elastically from its boundaries are…