Related papers: Generalized $(C, \lambda)$-structure for nonlinear…
We investigate the existence and regularity of locally invariant manifolds near an approximately invariant set that satisfies a geometric hyperbolicity condition with respect to an abstract ``generalized" dynamical system in Banach spaces.…
Let $\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism $f\in\Diff(M)$. We show that the space of invariant measures supported on $\Lambda$ coincides with the space of accumulation measures of time averages…
We prove the existence of measurable invariant manifolds for small perturbations of linear Random Dynamical Systems evolving on a Banach space and admitting a general type of dichotomy, both for continuous and discrete time. Moreover, the…
We introduce and study the notions of (generalized) hyperbolicity, topological stability and (uniform) topological expansivity for operators on locally convex spaces. We prove that every generalized hyperbolic operator on a locally convex…
In this paper we survey known results of characterizations of reflexive Banach spaces, which are based on convergence of usual and generalized arithmetic mean (or Ces\`aro sum), weakly compact subsets, affine sets in a Banach space or its…
The $C^1$-structurally stable diffeomorphims of a compact manifold are those that satisfy Axiom A and the strong transversality condition (AS). We generalize the concept of AS from diffeomorphisms to invariant compact subsets. Among other…
Given a category of objects, it is both useful and important to know if all the objects in the category may be realised as sub-objects -- via morphisms in the given category -- of a single object in that category enjoying some nice…
The standard theory of Banach spaces is built upon the notions of vector space, triangle inequality and Cauchy completeness. Here we propose a `hyperbolic' variant of this `elliptic' framework where general linear combinations are replaced…
In this paper structure of infinite dimensional Banach spaces is studied by using an asymptotic approach based on stabilization at infinity of finite dimensional subspaces which appear everywhere far away. This leads to notions of…
A well-known result in the area of dynamical systems asserts that any invertible hyperbolic operator on any Banach space is structurally stable. This result was originally obtained by P. Hartman in 1960 for operators on finite-dimensional…
$C^1$ linearization is of special significance because it preserves smooth dynamical behaviors and distinguishes qualitative properties in characteristic directions. However, $C^1$ smoothness is not enough to guarantee $C^1$ linearization.…
We consider group-valued cocycles over dynamical systems with hyperbolic behavior. The base system is either a hyperbolic diffeomorphism or a mixing subshift of finite type. The cocycle $A$ takes values in the group of invertible bounded…
In [Discrete Contin. Dyn. Syst. \textbf{15} (2006), no. 3, 811--818.] Xia introduced a simple dynamical density basis for partially hyperbolic sets of volume preserving diffeomorphisms. We apply the density basis to the study of the…
In this work we study certain invariant measures that can be associated to the time averaged observation of a broad class of dissipative semigroups via the notion of a generalized Banach limit. Consider an arbitrary complete separable…
In the first part of the paper we study the structure of Banach spaces with a conditional spreading basis. The geometry of such spaces exhibit a striking resemblance to the geometry of James' space. Further, we show that the averaging…
In this paper we extend M. Lyubich's recent results on the global hyperbolicity of renormalization of quadratic-like germs to the space of C^r unimodal maps with quadratic critical point. We show that in this space the bounded-type limit…
J. Mather characterized uniform hyperbolicity of a discrete dynamical system as equivalent to invertibility of an operator on the set of all sequences bounded in norm in the tangent bundle of an orbit. We develop a similar characterization…
Recently, the von Neumann-Jordan type constants C(X) has defined by Takahashi. A new skew generalized constant Cp({\lambda},\mu,X) based on C(X) constant is given in this paper. First, we will obtain some basic properties of this new…
We shall introduce the notion of $C^\infty$ logarithmic symplectic structures on a differentiable manifold which is an analog of the one of logarithmic symplectic structures in the holomorphic category. We show that the generalized complex…
Let $\mathcal{R}$ be a strongly compact $C^2$ map defined in an open subset of an infinite-dimensional Banach space such that the image of its derivative $D_F \mathcal{R}$ is dense for every $F$. Let $\Omega$ be a compact, forward invariant…