Related papers: Interactions between function theory and holomorph…
In this article we give an expository account of the holomorphic motion theorem based on work of M\`a\~n\'e-Sad-Sullivan, Bers-Royden, and Chirka. After proving this theorem, we show that tangent vectors to holomorphic motions have…
If the preimage of a four-point set under a meromorphic function belongs to the real line, then the image of the real line is contained in a circle in the Riemann sphere. We include an application of this result to holomorphic dynamics: if…
Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are…
We consider heavy-tailed observables maximised on a dynamically defined Cantor set and prove convergence of the associated point processes as well as functional limit theorems. The Cantor structure, and its connection to the dynamics,…
In earlier work we have given a Hamiltonian analysis of Yang-Mills theory in (2+1) dimensions showing how a mass gap could arise. In this paper, generalizing and covariantizing from the mass term in the Hamiltonian analysis, we obtain two…
We discuss the dynamics of the Dirac fermions in the general strong gravitational and electromagnetic fields. We derive the general Hermitian Dirac Hamiltonian and transform it to the Foldy-Wouthuysen representation for the spatially…
In this manuscript we systematically review known results of local dynamics of discrete local holomorphic dynamics near fixed points in one and several complex variables as well as the consequences in global dynamics.
Wiles' work on Fermat's last Theorem highlighted the power of $p$-adic methods to prove the existence of analytic continuations of $\zeta$ and $L$ functions. These methods have become considerably more sophisticated in recent years, and…
We build a statistical description of fermions, taking into account the spin degree of freedom in addition to the momentum of particles, and we detail its use in the context of the kinetic theory of gases of fermions particles. We show that…
We study the dynamics of holomorphic correspondences $f$ on a compact Riemann surface $X$ in the case, so far not well understood, where $f$ and $f^{-1}$ have the same topological degree. Under a mild and necessary condition that we call…
The relation between four-dimensional $SO(4)$ pure Yang-Mills theory and the gravity is discussed. The functional integral for Yang-Mills theory is rewritten in terms of the gravity metric and Riemann tensors. This relation is shown to also…
The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…
The paper reviews some parts of classical potential theory with applications to two dimensional fluid dynamics, in particular vortex motion. Energy and forces within a system of point vortices are similar to those for point charges when the…
This survey focuses on strong closing lemmas in Hamiltonian dynamics that are proved using spectral invariants (also known as action selectors) in symplectic geometry. We review strong closing lemmas in low-dimensional Hamiltonian dynamics…
MOG as a modified gravity theory is designed to be replaced with dark matter. In this theory, in addition to the metric tensor, a massive vector is a gravity field where each particle has a charge proportional to the inertial mass and…
The study of high-speed rotating matter is a crucial research topic in physics due to the emergence of novel phenomena. In this paper, we combined cranking covariant density functional theory (CDFT) with a similar renormalization group…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
Consider the overdamped limit for a system of interacting particles in the presence of hydrodynamic interactions. For two-body hydrodynamic interactions and one- and two-body potentials, a Smoluchowski-type evolution equation is rigorously…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
The "theory of open sub-functorial dynamics" is a new theory that defines interacting generalized dynamical systems. The interactions between these dynamics produce new dynamics which, of course, can then enter into other interactions. A…