Related papers: Minimal displacement set for weakly systolic compl…

We discuss about the denseness of the strong stable and unstable manifolds of partially hyperbolic diffeomorphisms. In this sense, we introduce a concept of m-minimality. More precisely, we say that a partially hyperbolic diffeomorphisms is…

A classical counterexample due to E. De Giorgi, shows that the weak maximum principle does not remain true for general linear elliptic differential systems. After that, there are some efforts to establish the weak maximum principle for…

A polysymplectic structure is a vector-valued symplectic form, that is, a closed nondegenerate 2-form with values in a vector space. We first outline the polysymplectic Hamiltonian formalism with coefficients in a vector space $V$, then…

We show that a connected finite topological space with $12$ or less points has a weak homotopy type of a wedge of spheres. In other words, we show that the order complex of a connected finite poset with $12$ or less points has a homotopy…

We show that nontrivial homoclinic trajectories of a family of discrete, nonautonomous, asymptotically hyperbolic systems parametrized by a circle bifurcate from a stationary solution if the asymptotic stable bundles Es(+{\infty}) and…

We investigate dynamically and statistically diffusive motion in a chain of linearly coupled 2-dimensional symplectic McMillan maps and find evidence of subdiffusion in weakly and strongly chaotic regimes when all maps of the chain possess…

Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…

We have researched the condition for symplectic discretization to preserve local boundedness for the space of 2-dimensional Hamiltonian dynamical systems in this paper.

We consider faithful actions of simple algebraic groups on self-dual irreducible modules, and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the…

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…

The optimal transportation problem defines a geometry of probability measures which leads to a definition for weighted averages (barycenters) of measures, finding application in the machine learning and computer vision communities as a…

We show that the systolic constant, the minimal entropy, and the spherical volume of a manifold depend only on the image of the fundamental class under the classifying map of the universal covering. Moreover, we compute the systolic…

In this paper the homology stability for symplectic groups over a ring with finite stable rank is established. First we develop a `nerve theorem' on the homotopy type of a poset in terms of a cover by subposets, where the cover is itself…

We study Krasnoselskii-Mann style iterative algorithms for approximating fixpoints of asymptotically weakly contractive mappings, with a focus on providing generalised convergence proofs along with explicit rates of convergence. More…

We introduce harmonic persistent homology spaces for filtrations of finite simplicial complexes. As a result we can associate concrete subspaces of cycles to each bar of the barcode of the filtration. We prove stability of the harmonic…

Ergodic optimization and discrete weak KAM theory are two parallel theories with several results in common. For instance, the Mather set is the locus of orbits which minimize the ergodic averages of a given observable. In the favorable…

On a complex symplectic manifold, we construct the stack of quantization-deformation modules, that is, (twisted) modules of microdifferential operators with an extra central parameter, a substitute to the lack of homogeneity. We also…

A field-theoretic description of the critical behaviour of the weakly disordered systems is given. Directly, for three- and two-dimensional systems a renormalization analysis of the effective Hamiltonian of model with replica symmetry…

We study simplicial complexes with a given number of vertices whose Stanley-Reisner ring has the minimal possible Betti numbers. We find that these simplicial complexes have very special combinatorial and topological structures. For…

We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting is called a strong…