Constructing Generalized Synchronization Manifolds by Manifold Equation

Constructing Generalized Synchronization Manifolds by Manifold Equation

Full understanding of synchronous behavior in coupled dynamical systems beyond the identical case requires an explicit construction of the generalized synchronization manifold, whether we wish to compare the systems or to understand their stability. Nonetheless, while synchronization has become an extremely popular topic, the bulk of the research in this area has been focused on the identical c...

On some generalized recurrent manifolds

‎The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds‎, ‎called‎, ‎super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [‎A.A‎. ‎Shaikh and A‎. ‎Patra‎, On a generalized class of recurrent manifolds‎, Arch‎. ‎Math‎. ‎(Brno) 46 (2010) 71--78‎.] and weakly generalized recurrent manifolds ...

Constructing Combinatorial 4-manifolds

Every closed oriented PL 4-manifold is a branched cover of the 4-sphere branched over a PL-surface with finitely many singularities by Piergallini [Topology 34(3):497-508, 1995]. This generalizes a long standing result by Hilden and Montesinos to dimension four. Izmestiev and Joswig [Adv. Geom. 3(2):191-225, 2003] gave a combinatorial equivalent of the Hilden and Montesinos result, constructing...

The Manifolds Covered by a Riemannian Homogeneous Manifold

Constructing a Fake 4-manifold by Gluck Construction to a Standard 4-manifold

LET S3 G S’ denote the twisted S3 bundle over S’. In this paper we will demonstrate an imbedding of a 2-sphere f:S* 4 S3 G S’ #S* x S* such that twisting S3 g S’ #S’ x S* along f(S*) (Gluck construction) produces a fake manifold M4. In fact M4 coincides with the fake S3 2 S’ #S* x S*‘s of [l] and 123. More specifically, if IV;= M-int(B3 g S’) (a fake B3 z S’ # S* x S*) and Q4 is the Cappell-Sha...