Related papers: Complex dynamics and invariant forms mod p

Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.

This paper contains an analysis of rank-k solutions in terms of Riemann invariants, obtained from interrelations between two concepts, that of the symmetry reduction method and of the generalized method of characteristics for first order…

In this talk we introduce the properties of scattering forms on the compactified moduli space of Riemann spheres with $n$ marked points. These differential forms are $\text{PSL}(2,\mathbb{C})$ invariant, their intersection numbers…

We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…

The model system manifesting phenomena peculiar to complex analytic maps is offered. The system is a non-autonomous ring cavity with nonlinear elements and filters,

Irreversible thermodynamics of simple fluids have been connected recently to the theory of dynamical systems and some interesting assumptions have been made about the nature of the associated invariant measures. We show that the tests of…

Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…

The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be…

We show that for a hyperbolic system of hydrodynamic type admitting n symmetries, there exists a coordinate system in which the generator of the system and all the symmetries are diagonal.

This paper studies the behavior of dynamical systems in non-compact spaces, specifically focusing on the concepts of global attractors and shadowing. Let $K$ be a compact global attractor. We show that the shadowing property holds in…

Let M be an analytic manifold modelled on an ultrametric Banach space over a complete ultrametric field. Let f be an analytic diffeomorphism from M onto itself and p be a fixed point of f. We discuss invariant manifolds around p, like…

Newtonian, Lagrangian, and Hamiltonian dynamical systems are well formalized mathematically. They give rise to geometric structures describing motion of a point in smooth manifolds. Riemannian metric is a different geometric structure…

This is an expository article, originally written in Japanese, on a dynamical system over a non-archimedean field. The main viewpoint is from complex and non-archimedean potential theories. After quickly introducing the Berkovich projective…

Hybrid (and impact) systems are dynamical systems experiencing both continuous and discrete transitions. In this work, we derive necessary and sufficient conditions for when a given differential form is invariant, with special attention…

We exhibit invariants of smooth projective algebraic varieties with integer values, whose nonvanishing modulo p prevents the existence of an action without fixed points of certain finite p-groups. The case of base fields of characteristic p…

Dynamics has been generalized to a noncommutative phase space. The noncommuting phase space is taken to be invariant under the quantum group $GL_{q,p}(2)$. The $q$-deformed differential calculus on the phase space is formulated and using…

The description of invariants of surfaces with respect to the motion groups is reduced to the description of invariants of parameterized surfaces with respect to the motion groups. Existence of a commuting system of invariant partial…

An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the finite-scale Hamiltonian dynamics is governed by…

We consider the question of computing invariant measures from an abstract point of view. We work in a general framework (computable metric spaces, computable measures and functions) where this problem can be posed precisely. We consider…

We compare modular forms of characteristic $p>0$ (i.e. Drinfeld's modular forms) and automorphic forms. We prove that spaces of these modular forms (which are of characteristic $p$) can be described by function spaces of characteristic…