Related papers: The Cyclic Hopf H mod K Theorem
The probabilistic description of finite classical systems often leads to linear kinetic equations. A set of physically motivated mathematical requirements is accordingly formulated. We show that it necessarily implies that solutions of such…
Let $G$ be a finite group and let $k$ be a field whose characteristic $p$ divides the order of $G$. Freyd's generating hypothesis for the stable module category of $G$ is the statement that a map between finite-dimensional $kG$-modules in…
In this paper we describe a method to estimate a neighborhood containing a periodic orbit of a given system of two ordinary differential equations. By using the theory of integral averages, the system of differential equations can be…
We propose a category which can serve as the category of coefficients for the cyclic homology HC_*(A) of an associative algebra A over a field k. The construction is categorical in nature, and essentially uses only the tensor category…
We consider a delay differential equation that occurs in the study of chronic myelogenous leukemia. After shortly reminding some previous results concerning the stability of equilibrium solutions, we concentrate on the study of stability of…
We study otopy classes of equivariant local maps and prove the Hopf type theorem for such maps in the case of a real finite dimensional orthogonal representation of a compact Lie group.
We give a systematic description of the cyclic cohomology theory of Hopf algebroids in terms of its associated category of modules. Then we introduce a dual cyclic homology theory by applying cyclic duality to the underlying cocyclic…
We define and study an equivariant $E$-theory with respect to coactions of Hopf $C^*$-algebras; we prove the Baaj-Skandalis duality in this setting. We show that the corresponding equivariant $KK$-theory of Baaj and Skandalis enjoys an…
A hamiltonian cycle system (HCS, for short) of a graph $\Gamma$ is a partition of the edges of $\Gamma$ into hamiltonian cycles. A HCS is cyclic when it is invariant under a cyclic permutation of all the vertices of $\Gamma$; the existence…
We define a Hopf cyclic (co)homology theory in an arbitrary symmetric strict monoidal category. Thus we unify all different types of Hopf cyclic (co)homologies under one single universal theory. We recover Hopf cyclic (co)homology of module…
Let $k$ be an arbitrary field of characteristic $p$ and let $G$ be a finite group. We investigate the representation type, derived representation type, and singularity category of the $k$-linear (cohomological) Mackey algebra. We classify…
By a nondegenerate $k$-parameterized family $K$ of periodic solutions we understand the situation when the geometric multiplicity of the multiplier +1 of the linearized on $K$ system equals to $k.$ Bifurcation of asymptotically stable…
An equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a…
We associate canonically a cyclic module to any Hopf algebra endowed with a modular pair, consisting of a group-like element and a character, in involution. This provides the key construct allowing to extend cyclic cohomology to Hopf…
In this paper, we study the existence of bifurcation of a van der Pol-Duffing oscillator with quintic terms and its quasi-periodic solutions by means of qualitative and bifurcation theories. Firstly, we analyze the autonomous system and…
We prove that time-periodic solutions arise via Hopf bifurcation in a finite closed system of coagulation-fragmentation equations. The system we treat is a variant of the Becker-Doering equations, in which clusters grow or shrink by…
This book introduces a new context for global homotopy theory, i.e., equivariant homotopy theory with universal symmetries. Many important equivariant theories naturally exist not just for a particular group, but in a uniform way for all…
An SIS model is investigated in which the infective individuals are assumed to have an infection-age structure. The model is formulated as an abstract non-densely defined Cauchy problem. We study some dynamical properties of the model by…
We show that a surjective homomorphism $\varphi \colon \Gamma \to K$ of (discrete) groups induces an isomorphism $H^\bullet_b(K; V) \to H^\bullet_b(\Gamma; \varphi^{-1} V)$ in bounded cohomology for all dual normed $K$-modules $V$ if and…
Given a good homology theory E and a topological space X, the E-homology of X is not just an E_{*}-module but also a comodule over the Hopf algebroid (E_{*}, E_{*}E). We establish a framework for studying the homological algebra of…