Related papers: Cohomological equations for linear involutions
In this paper we give sufficient conditions for existence of a solution of cohomological equation for suspension flows over automorphisms of Markov compacta, which were introduced by Vershik and Ito. The main result (Theorem 1) can be…
We extend some results of Marmi--Moussa--Yoccoz on the cohomological equations and local conjugacy classes of interval exchange maps of restricted Roth type. In particular, we answer a question of Krikorian about the codimension of the…
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 provide a geometrical interpretation for the series of transformations used by Sakovich to map the third-order nonlinear evolution equation obtained by Chou and Qu to the mKdV equation. We also discuss its bi-Hamiltonian integrability as…
We show cocycle stability for linear maps with a weak irreducibility condition and their jointly integrable perturbations.
In our article "A tree of linearisable second-order evolution equations by generalised hodograph transformations" [J. Nonlin. Math. Phys. {\bf 8} (2001), 342-362] we presented a tree of linearisable (C-integrable) second-order evolution…
Discusses several integrability tests for nonlinear evolution equations.
We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of a discrete data determined by the images of parameters. In similar terms, we…
We introduce middle convolution for systems of linear differential equations with irregular singular points, and we presend a tentative definition of the index of rigidity for them. Under some assumption, we show a list of terminal patterns…
We discuss inverse problems to finding the time-dependent coefficient for the multidimensional Cauchy problems for both strictly hyperbolic equations and polyharmonic heat equations. We also extend our techniques to the general inverse…
The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable evolution equations which preserve local…
We prove that the solutions of the cohomological equation for Roth type interval exchange maps are H\"older continuous provided that the datum is of class $C^r$ with $r>1$ and belongs to a finite-codimension linear subspace.
The survey provides classification results for integrable one-field evolution equations of orders 2, 3 and 5 with the constant separant. The classification is based on necessary integrability conditions following from the existence of the…
We present a study of the homological algebra of bimodules over $A_\infty$-algebras endowed with an involution. Furthermore we introduce a derived description of Hochschild homology and cohomology for involutive $A_\infty$-algebras.
These are lecture notes from the IMPANGA 2010 Summer School. The lectures survey some of the main features of equivariant cohomology at an introductory level. The first part is an overview, including basic definitions and examples. In the…
We give a natural cohomological interpretation of Letzter-Makar-Limanov invariants for rings of differential operators on algebraic curves.
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
A typical interval exchange transformation has an infinite sequence of matrices associated to it by successive iterations of Rauzy induction. In 2010, W. A. Veech answered a question of A. Bufetov by showing that the interval exchange…
We provide base change theorems, projection formulae and Verdier duality for both cohomology and homology in the context of finite topological spaces
The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary functions is obtained by requiring presence…