Related papers: Dynamics on dendrites with closed endpoint sets
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…
We prove that a zero topological entropy continuous tree map always displays zero topological sequence entropy when it is restricted to its non-wandering and chain recurrent sets. In addition, we show that a similar result is not possible…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system…
In this work we present a novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems. It extends a classical subdivision technique [Dellnitz/Hohmann 1997] for the computation of such…
The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter…
In the limit where the bending modulus vanishes, we construct layer configurations with arbitrary dislocation textures by exploiting a connection between uniformly-spaced layers in two dimensions and developable surfaces in three…
This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact…
In this paper, we study various chaos of topological group or semigroup actions.
We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the…
We construct large families of initial data sets for the vacuum Einstein equations with positive cosmological constant which contain exactly Delaunay ends; these are non-trivial initial data sets which coincide with those for the…
Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many non-isomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric…
We study uniqueness of Dirichlet problems of second order divergence-form elliptic systems with transversally independent coefficients on the upper half-space in absence of regularity of solutions. To this end, we develop a substitute for…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
By a result of Blokh from 1984, every transitive map of a tree has the relative specification property, and so it has finite decomposition ideal, positive entropy and dense periodic points. In this paper we construct a transitive dendrite…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
We survey the connections between entropy, chaos, and independence in topological dynamics. We present extensions of two classical results placing the following notions in the context of symbolic dynamics: 1. Equivalence of positive entropy…
A geometric charactrization of the equation found by Hietarinta and Viallet, which satisfies the singularity confinement criterion but which exhibits chaotic behavior, is presented. It is shown that this equation can be lifted to an…
We show a flexibility result in the context of generalized entropy. The space of dynamical systems we work with is, homeomorphisms on the sphere whose non-wandering set consist in only one fixed point.