Related papers: Aperiodic Flows on Finite Semigroups: Foundations …

The Adler-Kostant-Symes theorem yields isospectral hamiltonian flows on the dual $\tilde\grg^{+*}$ of a Lie subalgebra $\tilde\grg^+$ of a loop algebra $\tilde\grg$. A general approach relating the method of integration of Krichever,…

We present a series of analytically solvable axisymmetric flows on the torus geometry. For the single-component flows, we describe the propagation of sound waves for perfect fluids, as well as the viscous damping of shear and longitudinal…

The problem of a travelling wave over an arbitrary quasi-flat bathymetry in a semi infinite channel is studied in the shallow-water formulation. It is shown how the streamfunction can be cast, in the vicinity of an elliptic equilibrium for…

We study the classification of the pairs $(N, \,X)$ where $N$ is a Stein surface and $X$ is a complete holomorphic vector field with isolated singularities on $N$. We describe the role of transverse sections in the classification of $X$ and…

Let $S$ be a finite semigroup. In this paper we introduce the functions $\phi_s:S^* \to S^*$, first defined by Rhodes, given by $\phi_s([a_1,a_2 ,...,a_n]) = [sa_1,sa_1a_2,..., sa_1a_2 ... a_n]$. We show that if $S$ is a finite aperiodic…

A computational flow is a pair consisting of a sequence of computational problems of a certain sort and a sequence of computational reductions among them. In this paper we will develop a theory for these computational flows and we will use…

We apply the functional renormalization group theory to the dynamics of first-order phase transitions and show that a potential with all odd-order terms can describe spinodal decomposition phenomena. We derive a momentum-dependent dynamic…

We study a family of fermionic extensions of the Camassa-Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently hamiltonian, describing geodesic flow with respect to an H^1 metric on the…

On a smooth compact Riemannian manifold without boundary, we construct a finite dimensional cohomological complex of currents that are invariant by an Axiom A flow verifying Smale's transversality assumptions. The cohomology of that complex…

Morse theory relates algebraic topology invariants and the dynamics of the gradient flow of a Morse function, allowing to derive information about one out of the other. In the case of the homology, the construction extends to much more…

This paper develops the theory of affine Euler-Poincar\'e and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids,…

The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup property arises naturally when the solutions of a differential…

We are motivated by a conjecture of A. and S. Katok to study the smooth cohomologies of a family of Weyl chamber flows. The conjecture is a natural generalization of the Livshitz Theorem to Anosov actions by higher-rank abelian groups; it…

For certain pseudo-Anosov flows $\phi$ on closed $3$-manifolds, unpublished work of Agol--Gu\'eritaud produces a veering triangulation $\tau$ on the manifold $M$ obtained by deleting $\phi$'s singular orbits. We show that $\tau$ can be…

We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space which evolve by an arbitrary (non-homogeneous) function of the radii of curvature. The associated flow of the radii of…

We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional…

Inspired by work of Besson-Courtois-Gallot, we construct a flow called the natural flow on a non-positively curved Riemannian manifold $M$. As with the natural map, the $k$-Jacobian of the natural flow is directly related to the critical…

In this paper, we study flows and semiflows defined on any given finite topological $T_0$-space $X$. We show that there exist non-trivial semiflows on $X$, unless $X$ is a minimal finite space. Specifically, non-trivial semiflows exist if…

We revisit the existence of monotonic quantities along renormalization group flows using only the Null Energy Condition and the Ryu-Takayanagi formula for the entanglement entropy of field theories with anti-de Sitter gravity duals. In…

We generalize a well known periodicity lemma from the case of free groups to the case of acylindrically hyperbolic groups. This generalization will be used later to describe solutions of certain equations in acylindrically hyperbolic groups…