This paper continues our investigation of the dynamics of polynomial diffeomorphisms of C 2 carried out in [BS1-7]. There are several reasons why the polynomial diffeomorphisms of C 2 form an interesting family of dynamical systems. Not the least of these is the fact that there are connections with two other areas of dynamics: polynomial maps of C and diffeo-morphisms of R 2 , which have each r...

We prove a conjecture of Griffiths on the quasi-projectivity images period maps using algebraization results arising from o-minimal geometry. Specifically, we first develop theory analytic spaces and coherent sheaves that are definable with respect to given structure, GAGA-type theorem algebraizing complex algebraic spaces. then combine this theorems Artin show proper algebraic. Applying maps, ...

In this paper, we define the concept of probabilistic like Menger (probabilistic like quasi Menger) space (briefly, PLM-space (PLqM-space)). We present some coupled fixed point and fixed point results for certain contraction type maps in partially order PLM-spaces (PLqM- spaces).

208 NOTICES OF THE AMS VOLUME 51, NUMBER 2 As far as I know, the notion of a quasi-morphism does not have much to do with category theory. This very natural idea underlies several interesting recent developments at the crossroads of algebra, topology, geometry, and dynamics. Other, perhaps better, names currently in use for the same concept are quasi-homomorphism and pseudo-character. Let G be ...

In this paper, we consider the system of vector quasi-equilibrium problems with or without involving -condensing maps and prove the existence of its solution. Consequently, we get existence results for a solution to the system of vector quasi-variational-like inequalities. We also prove the equivalence between the system of vector quasi-variational-like inequalities and the Debreu type equilibr...

Quasi-Borel spaces are a new mathematical structure that supports higher-order probability theory, first-order iteration, and modular semantic validation of Bayesian inference algorithms with continuous distributions. Like a measurable space, a quasi-Borel space is a set with extra structure suitable for defining probability and measure distributions. But unlikemeasurable spaces, quasi-Borel sp...