We prove some properties of analytic multiplicative and sub-multiplicative cocycles. The results allow to construct natural invariant analytic sets associated to complex dynamical systems. AMS classification: 37F, 32H Key-words: multiplicative cocycle, sub-multiplicative cocycle, exceptional set

We present a formula expressing Earle’s twisted 1-cocycle on the mapping class group of a closed oriented surface of genus ≥ 2 relative to a fixed base point, with coefficients in the first homology group of the surface. For this purpose we compare it with Morita’s twisted 1-cocycle which is combinatorial. The key is the computation of these cocycles on a particular element of the mapping class...

We present a formula expressing Earle’s twisted 1-cocycle on the mapping class group of a closed oriented surface of genus ≥ 2 relative to a fixed base point, with coefficients in the first homology group of the surface. For this purpose we compare it with Morita’s twisted 1-cocycle which is combinatorial. The key is the computation of these cocycles on a particular element of the mapping class...

We prove that certain topologically mixing two-dimensional shifts of finite type have a ‘fundamental’ 1-cocycle with the property that every continuous 1-cocycle on the shift space with values in a discrete group is continuously cohomologous to a homomorphic image of the fundamental cocycle. These fundamental cocycles are closely connected with representations of the shift space by Wang tilings...

Let H be a Hopf algebra over a commutative ring k with unity and σ : H ⊗ H −→ k be a cocycle on H. In this paper, we show that the Yetter-Drinfeld module category of the cocycle deformation Hopf algebra H is equivalent to the Yetter-Drinfeld module category of H. As a result of the equivalence, the “quantum Brauer” group BQ(k,H) is isomorphic to BQ(k,H). Moreover, the group Gal(HR) constructed ...

We consider the cohomology of two-dimensional subshifts, and develop a new approach to proving that every cocycle is trivial (i.e. cohomologous to a homomorphism). We introduce semi-safe subshifts which, roughly speaking, have the property that some symbol can surround all allowed blocks in at least one horizontal and one vertical direction. We prove that for such subshifts, every locally const...

In this paper, firstly we introduce the concept of norm-to-weak continuous cocycle in Banach space and give a technical method to verify this kind of continuity, then we obtain some abstract results for the existence of pullback attractors about this kind of cocycle, using the measure of noncompactness. As an application, we prove the existence of pullback attractors in H 1 0 of the cocycle ass...

We introduce a quantum double quasitriangular quasi-Hopf algebra D(H) associated to any quasi-Hopf algebra H. The algebra structure is a cocycle double cross product. We use categorical reconstruction methods. As an example, we recover the quasi-Hopf algebra of Dijkgraaf, Pasquier and Roche as the quantum double D(G) associated to a finite group G and group 3-cocycle φ. We also discuss D(Ug) as...

In this paper, we study the dynamics of a two-dimensional stochastic Navier-Stokes equation on a smooth domain, driven by multiplicative white noise. We show that solutions of the 2D Navier-Stokes equation generate a perfect and locally compacting C1,1 cocycle. Using multiplicative ergodic theory techniques, we establish the existence of a discrete non-random Lyapunov spectrum for the cocycle. ...

Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in Quantum Field Theory. This representation permutes “Gaussian” elements in the fermion Fock space, and is necessarily projective: we compute its cocycle at the group level, and obtain Schwinger terms and anomalies from infinitesimal versions of this cocycle. Quantization, in this framewor...