Some theorems on projective hyperbolicity

Some Immersion Theorems for Projective Spaces

Adem and Gitler showed in [4] and [7] that RPn has a best possible immersion in R2n'i for n=X mod 4 and <*(«) = 3. These results are interesting only for small values of a(«) due to Milgram's construction of linear immersions in [21]. The method of proof consists of expressing certain obstructions to the lifting of an appropriate map by AdamsMaunder operations and then evaluating these operatio...

Hadamard–perron Theorems and Effective Hyperbolicity

We prove several new versions of the Hadamard–Perron Theorem, which relates infinitesimal dynamics to local dynamics for a sequence of local diffeomorphisms, and in particular establishes the existence of local stable and unstable manifolds. Our results imply the classical Hadamard–Perron Theorem in both its uniform and non-uniform versions, but also apply much more generally. We introduce a no...

Stability Theorems and Hyperbolicity in Dynamical Systems

We present an approach to proving structural stability and semi-stability theorems for diffeomorphisms and flows using the idea of shadowing an e-chain. We treat the cases when the whole manifold is hyperbolic and when the chain recurrent set is hyperbolic and the strong transversality condition is satisfied. The last two sections discuss the progress made on the converse to the structural stab...

Some Theorems on Coverings

Some Theorems on Continua

PROOF. Let {Gn} and {Hn} denote monotonie decreasing sequences of open sets which close down upon .Pi and F2 respectively. We may suppose that d and Hi are so chosen that G i # i = 0. Now, by Mullikin's theorem, there is a connected subset of C— C(Gw+27n) which has a limit point in Gn and a limit point in Hn. The closure of such a connected set is a subcontinuum of C which "extends" from Gn to ...