Related papers: H\'enon maps: a list of open problems
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
We draw two incomplete, biased maps of challenges in computational complexity lower bounds.
Some positive answers to the problem of endowing a dynamical system with a Hamiltonian formulation are presented within the class of Poisson structures in a geometric framework. We address this problem on orientable manifolds and by using…
Three open problems in analysis are formulated: 1. Injectivity of Radon transform 2. A uniqueness problem for an elliptic system of PDE 3. A problem in operator theory
This survey explores a range of classical findings and recent developments related to our understanding of astheno-K\"ahler manifolds. Furthermore, we provide various examples of astheno-K\"ahler manifolds and analyze the challenges…
In the field of holomorphic dynamics in one complex variable, hedgehog is the local invariant set arising about a Cremer point and endowed with a very complicate shape as well as relating to very weak numerical conditions. We give a…
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 provide necessary and sufficient conditions for a set-valued mapping between finite dimensional spaces to be directionally open by relating this property with directional regularity, H\"older continuity of the inverse mapping,…
We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods, group-theoretic and coming from algebraic and arithmetic…
We give a brief survey of recent results on word maps on simple groups and polynomial maps on simple associative and Lie algebras. Our focus is on parallelism between these theories, allowing one to state many new open problems and giving…
We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H the problem is either NP-complete, NL-complete, L-complete or is…
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…
This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.
We discuss several approaches to motivic complexes and explicit constructions of the regulator maps from the motivic complexes to Deligne complexes.
Maps have always been an essential component of autonomous driving. With the advancement of autonomous driving technology, both the representation and production process of maps have evolved substantially. The article categorizes the…
We study the evolution equations for a regularized version of Dirac-harmonic maps from closed Riemannian surfaces. We establish the existence of a global weak solution for the regularized problem, which is smooth away from finitely many…
In this paper we analyze chaotic dynamics for two dimensional nonautonomous maps through the use of a nonautonomous version of the Conley-Moser conditions given previously. With this approach we are able to give a precise definition of what…
The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are…
For any real diagonalizable matrix with complex eigenvalues we provide a real, coordinate free decomposition with a clear geometric interpretation.
We introduce a class of volume-contracting surface diffeomorphisms whose dynamics is intermediate between one-dimensional dynamics and general surface dynamics. For that type of systems one can associate to the dynamics a reduced…