Related papers: Katok-Hasselblatt-kinematic expansive flows
For a continuous curve of families of Dirac type operators we define a higher spectral flow as a $K$-group element. We show that this higher spectral flow can be computed analytically by $\heta$-forms, and is related to the family index in…
We discuss $(K,N)$-convexity and gradient flows for $(K,N)$-convex functionals on metric spaces, in the case of real $K$ and negative $N$. In this generality, it is necessary to consider functionals unbounded from below and/or above,…
We construct a Grassmannian-like formulation for the potential KP-hierarchy including additional ``negative'' flows. Our approach will generalize the notion of a tau-function to include negative flows. We compare the resulting hierarchy…
We introduce a new variational method for finding periodic orbits of flows and spatio-temporally periodic solutions of classical field theories, a generalization of the Newton method to a flow in the space of loops. The feasibility of the…
A bi--Hamiltonian formulation for stationary flows of the KdV hierarchy is derived in an extended phase space. A map between stationary flows and restricted flows is constructed: in a case it connects an integrable Henon--Heiles system and…
In this paper, we report an interesting kinematic phenomenon around the halos' edge related to the splashback radius. After the shell-crossing, cosmic flow exhibits various rotational morphologies via stream-mixing. Vorticity is generated…
In this paper geology and planetology are considered using new conceptual basis of high-speed flow dynamics. Recent photo technics allow to see all details of a flow, 'cause the flow is static during very short time interval. On the other…
We develop an abstract theory of flows of geometric $H$-structures, i.e., flows of tensor fields defining $H$-reductions of the frame bundle, for a closed and connected subgroup $H\subset SO(n)$, on any connected and oriented $n$-manifold…
New elementary, self-contained proofs are presented for the topological and the smooth classification theorems of linear flows on finite-dimensional normed spaces. The arguments, and the examples that accompany them, highlight the…
The paper develops and studies a very general notion of dichotomy, referred to as "nonuniform $(h,k,\mu,\nu)$-dichotomy". The new notion contains as special cases most versions of dichotomy existing in the literature. The paper then…
We consider Kasner space-time describing anisotropic three dimensional expansion of the fluid and obtain the dissipative evolution equations for shear stress tensor and energy density from kinetic theory. For this, we use the iterative…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
In this two-parts paper, we present a systematic procedure to extend the known Hamiltonian model of ideal inviscid fluid flow on Riemannian manifolds in terms of Lie-Poisson structures to a port-Hamiltonian model in terms of Stokes-Dirac…
We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebin's long-time existence result for geodesics on…
In 2005, the paper "Fraiss\'e limits, Ramsey theory, and topological dynamics of automorphism groups" [KPT] by Kechris, Pestov and Todorcevic provided a powerful tool to compute an invariant of topological groups known as the universal…
Recently, an increasing interest in astrophysical as well as laboratory plasmas has been manifested in reference to the existence of relativistic flows, related in turn to the production of intense electric fields in magnetized systems.…
Self-similarity in general relativity is briefly reviewed and the differences between self-similarity of the first kind and generalized self-similarity are discussed. The covariant notion of a kinematic self-similarity in the context of…
Katok's special representation theorem states that any free ergodic measure-preserving $\mathbb{R}^{d}$-flow can be realized as a special flow over a $\mathbb{Z}^{d}$-action. It provides a multidimensional generalization of the "flow under…
We consider the local kinematics at fluid interfaces in two-phase flows within the sharp interface framework. In the considered case with phase change and slip at the interface, the governing velocity field is discontinuous at the phase…
This paper introduces Higher Gauge Flow Models, a novel class of Generative Flow Models. Building upon ordinary Gauge Flow Models (arXiv:2507.13414), these Higher Gauge Flow Models leverage an L$_{\infty}$-algebra, effectively extending the…