相关论文: Dimension groups for interval maps II: the transit…

Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…

We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…

We study the measurable dynamics of transformations on profinite groups, in particular of those which factor through sufficiently many of the projection maps; these maps generalize the 1-Lipschitz maps on $\mathbb Z_p$.

The exponential map that characterises the flows of vector fields is the key in understanding the basic structural attributes of control systems in geometric control theory. However, this map does not exists due to the lack of completeness…

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…

Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a…

We give sufficient conditions for a finite metric space to be determined by the magnitude function. In particular, a generic finite metric space such that the distances between the points are rationally independent is determined by the…

Two kinds of maps that describe evolution of states of a subsystem coming from dynamics described by a unitary operator for a larger system, maps defined for fixed mean values and maps defined for fixed correlations, are found to be quite…

We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide some examples to discussion the possible…

We study shadowing-type properties for set-valued dynamical systems. In particular, we investigate the periodic shadowing property and its relationship with expansivity and chain transitivity. We establish that for positively expansive…

A monomial algebra is the quotient of a polynomial algebra by an ideal generated by monomials. We prove that finite-dimensional monomial algebras are characterized by their automorphism group among finite-dimensional, local algebras with…

The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit a transitive group of isometries are obtained. These conditions are Intrinsic, Deductive, Explicit and ALgorithmic, and they offer an IDEAL labeling…

A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…

We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.

To a given tiling a non commutative space and the corresponding C*-algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for…

The union of a directed family of topological groups can be equipped with two noteworthy topologies: the finest topology making each injection continuous, and the finest group topology making each injection continuous. This begs the…

A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…

We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant.…

Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…