Related papers: Pseudo-simple heteroclinic cycles in $R^4$

We develop a renormalisation group approach to deriving the asymptotics of the spectral gap of the generator of Glauber type dynamics of spin systems with strong correlations (at and near a critical point). In our approach, we derive a…

Homoclinic and heteroclinic orbits provide a skeleton of the full dynamics of a chaotic dynamical system and are the foundation of semiclassical sums for quantum wave packet, coherent state, and transport quantities. Here, the homoclinic…

This article concerns arbitrary finite heteroclinic networks in any phase space dimension whose vertices can be a random mixture of equilibria and periodic orbits. In addition, tangencies in the intersection of un/stable manifolds are…

Given a graph $\Gamma = (V, E)$ on $n$ vertices and $m$ edges, we define the Erd\H{o}s-R\'{e}nyi graph process with host $\Gamma$ as follows. A permutation $e_1,\dots,e_m$ of $E$ is chosen uniformly at random, and for $t\leq m$ we let…

We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the…

Let $\Gamma({\mathcal{W}})$ be the Cayley graph of a finite Weyl groupoid ${\mathcal{W}}$. In this paper, we show an existence of a Hamitonian cycle of $\Gamma({\mathcal{W}})$ for any ${\mathcal{W}}$. We exatctly draw a Hamiltonian cycle of…

The various nesting and pairing instabilities of the generalized Van Hove scenario can be classified via an SO(8) spectrum-generating algebra. An SO(6) subgroup is an approximate symmetry group of the model, having two 6-dimensional…

Let G be a semisimple Lie group with no compact factors, K a maximal compact subgroup of G, and $\Gamma$ a lattice in G. We study automorphic forms for $\Gamma$ if G is of real rank one with some additional assumptions, using dynamical…

We evaluate the variance of coefficients of the characteristic polynomial for binary quantum graphs using a dynamical approach. This is the first example where a spectral statistic can be evaluated in terms of periodic orbits for a system…

Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…

A real semisimple Lie group G_0 embedded in its complexification G has only finitely many orbits in any G-fag manifold Z = G/Q. The complex geometry of its open orbits D (flag domains) is studied from the point of view of compact complex…

Graph dynamical systems (GDSs) can be used to describe a wide range of distributed, nonlinear phenomena. In this paper we characterize cycle equivalence of a class of finite GDSs called sequential dynamical systems SDSs. In general, two…

We obtain slow dynamics for self-adjoint semigroups and unitary evolution groups. For semigroups, the slow dynamics is for orbits, and for the average return probability in the case of unitary evolution groups. We present an application to…

Let H be a 3-uniform hypergraph with N vertices. A tight Hamilton cycle C \subset H is a collection of N edges for which there is an ordering of the vertices v_1, ..., v_N such that every triple of consecutive vertices {v_i, v_{i+1},…

Understanding the hydrogen atom has been at the heart of modern physics. Exploring the symmetry of the most fundamental two body system has led to advances in atomic physics, quantum mechanics, quantum electrodynamics, and elementary…

We prove necessary and sufficient conditions for a smooth surface in a 4-manifold X to be pseudoholomorphic with respect to some almost complex structure on X. This provides a systematic approach to the construction of pseudoholomorphic…

Let $(M,\tau,\sigma,\Gamma)$ be a (finite) von Neumann dynamical system and let $N$ be a $\Gamma$-invariant unital von Neumann subalgebra of $M$. If $V\subset L^2(M)$ is a right $N$-submodule whose projection $p_V$ has finite trace in $<…

We consider the dynamics of bodies with "active" microstructure described by vector-valued phase fields. For waves with time-varying amplitude, the associated evolution equation involves a matrix that can be non-normal, depending on the…

Consider $\operatorname{Sym}(n)$, endowed with the normalized Hamming metric $d_n$. A finitely-generated group $\Gamma$ is \emph{P-stable} if every almost homomorphism $\rho_{n_k}\colon \Gamma\rightarrow\operatorname{Sym}(n_k)$ (i.e., for…

This short note studies $C^{\infty}$-smooth cocycles in $\mathbb{T}\times SO(3)$ that have $0$ degree and are non-homotopic to constants. The study picks up from where the author's PhD thesis left the subject, and shows that, under a…