Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNonexistence of spectral gaps in Holder spaces for continuous time dynamical systems
56
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We show that there is a natural restriction on the smoothness of spaces where the transfer operator for a continuous dynamical system has a spectral gap. Such a space cannot be embedded in a Holder space with Holder exponent greater than 1/2 unless it consists entirely of coboundaries.
rate research
Read More
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with collaborators formalized these kinds of structures (systems of systems) as algebras over presentable colored operads. It is also very useful to consider maps between dynamical systems. This amounts to viewing dynamical systems as objects in an appropriate category. This is the point taken by DeVille and Lerman in the study of dynamics on networks. The goal of this paper is to describe an algebraic structure that encompasses both approaches to systems of systems. To this end we replace the monoidal category of wiring diagrams by a monoidal double category whose objects are surjective submersions. This allows us, on one hand, build new large open systems out of collections of smaller open subsystems and on the other keep track of maps between open systems. As a special case we recover the results of DeVille and Lerman on fibrations of networks of manifolds.
For a topological group G, we show that a compact metric G-space is tame if and only if it can be linearly represented on a separable Banach space which does not contain an isomorphic copy of $l_1$ (we call such Banach spaces, Rosenthal spaces). With this goal in mind we study tame dynamical systems and their representations on Banach spaces.
We prove quench
The present note refers to a result proposed in [Elhadj and Sprott, 2012], and shows that the Theorem therein is not correct. We explain that a proof of that Theorem cannot be given, as the statement is not correct, and we underline a mistake occurring in their proof. Since this note is supplementary to [Elhadj and Sprott, 2012], the reader should consult this paper for further explanations of the matter and the symbols used.
We demonstrate how recent work of Favre and Gauthier, together with a modification of a result of the author, shows that a family of polynomials with infinitely many post-critically finite specializations cannot have any periodic cycles with multiplier of very low degree, except those which vanish, generalizing results of Baker and DeMarco, and Favre and Gauthier.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
