Related papers: Virtually expanding dynamics

We consider the dynamics of a meromorphic map on a compact kahler surface whose topological degree is smaller than its first dynamical degree. The latter quantity is the exponential rate at which its iterates expand the cohomology class of…

Differentially positive systems are the nonlinear systems whose linearization along trajectories preserves a cone field on a smooth Riemannian manifold. One of the embryonic forms for cone fields in reality is originated from the general…

With the aim of derive a quasi-monomiality formulation in the context of discrete hypercomplex variables, one will amalgamate through a Clifford-algebraic structure of signature $(0,n)$ the umbral calculus framework with Lie-algebraic…

The expansion of a superbubble is investigated both analytically and numerically. Our model implements the thin layer approximation in a vertical profile of density as given by an isothermal self-gravitating disk. A precise comparison with…

We consider the Dirichlet-Neumann operator for a nearly spherical domain in R^n, and prove sharp analytic and tame estimates in Sobolev class. The novelty of this paper concerns technical improvements, the most important of which are the…

In this work, we continue our study on discrete abstractions of dynamical systems. To this end, we use a family of partitioning functions to generate an abstraction. The intersection of sub-level sets of the partitioning functions defines…

Let $(X,\omega)$ be a compact symplectic manifold, $L$ be a Lagrangian submanifold and $V$ be a codimension 2 symplectic submanifold of $X$, we consider the pseudoholomorphic maps from a Riemann surface with boundary…

We introduce almost diagonal matrices in the setting of (anisotropic) discrete homogeneous Triebel-Lizorkin type spaces and homogeneous modulation spaces, and it is shown that the class of almost diagonal matrices is closed under matrix…

We study the size of \emph{dynamical covering sets} on a self-similar set. Dynamical covering sets are limsup sets generated by placing shrinking target sets around points along an orbit in a dynamical system. In the case when the target…

For any symplectic manifold, Hamiltonian diffeomorphism group contains a subset which consists of times one flows of autonomous(time-independent) Hamiltonian vector fields. Polterovich and Shelukhin proved that the complement of autonomous…

We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a CAT(0) cubical complex. Under suitable assumptions on the peripheral subgroups, these groups are residually finite and…

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…

We investigate the large scale geometry of certain metric spaces through the lens of dynamics. Our approach establishes a close connection between large scale dynamical phenomena and operator algebras by characterizing various large scale…

It is shown that max-preserving maps (or join-morphisms) on the positive orthant in Euclidean $n$-space endowed with the component-wise partial order give rise to a semiring. This semiring admits a closure operation for maps that generate…

The subleading eigenvalues and associated eigenfunctions of the Perron-Frobenius operator for 2-dimensional area-preserving maps are numerically investigated. We closely examine the validity of the so-called Ulam method, a numerical scheme…

We study the possible dynamical degrees of automorphisms of the affine space $\mathbb{A}^n$. In dimension $n=3$, we determine all dynamical degrees arising from the composition of an affine automorphism with a triangular one. This…

The spectral properties of the Frobenius-Perron operator of one-dimensional maps are studied when approaching a weakly intermittent situation. Numerical investigation of a particular family of maps shows that the spectrum becomes extremely…

In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…

We show that a fairly arbitrary Frechet space topology on the space of holomorphic functions on a domain controls the topology of uniform convergence on compact sets. In fact it turns out that the result we present can be proved more simply…

Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…