Related papers: Katok-Hasselblatt-kinematic expansive flows
Carnot groups are subRiemannian manifolds. As such they admit geodesic flows, which are left-invariant Hamiltonian flows on their cotangent bundles. Some of these flows are integrable. Some are not. The space of k-jets for real-valued…
In this paper, we introduce the notion of dynamical coherence for a partially hyperbolic flow $(\varphi^t)$ on a smooth compact manifold $M$, and prove it under the assumption that there exists a compact foliation with trivial holonomy…
Building on the dictionary between Kleinian groups and rational maps, we establish new connections between the theories of hyperbolic groups and certain iterated maps, regarded as dynamical systems. In order to make the exposition…
Hamilton flows on K\"ahler manifold for which all trajectories are $H$-planar curves (complex analog of geodesics) are considered. These flows are called $H$-planar. The equation which has to obey the Hamiltonian of $H$-planar Hamilton flow…
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…
Nonlinear idempotent operator instead of a linear projection is introduced to derive kinetic models for dense fluids. A new lattice Boltzmann model for compressible two-phase flow is derived based on the Enskog--Vlasov kinetic equation as…
Kinetic theory offers a promising alternative to conventional turbulence modelling by providing a mesoscopic perspective that naturally captures non-equilibrium physics such as non-Newtonian effects. In this work, we present an extension…
J. Streets and G. Tian recently introduced symplectic curvature flow, a geometric flow on almost K\"ahler manifolds generalising K\"ahler-Ricci flow. The present article gives examples of explicit solutions to this flow of non-K\"ahler…
We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of completely integrable Hamiltonian systems are investigated.…
Steady shearing and planar extension are commonly viewed as two distinct types of flow field, especially in the context of probing the rheology of complex fluids. By leveraging the kinematic equivalence between the two flows, we derive an…
We introduce two notions of hyperbolicity for not necessarily K\"ahler $n$-dimensional compact complex manifolds $X$. The first, called {\it balanced hyperbolicity}, generalises Gromov's K\"ahler hyperbolicity by means of Gauduchon's…
We derive the pressure tensor and the heat flux to accompany the new macroscopic conservation equations that we developed previously in a volume-based kinetic framework for gas flows. This kinetic description allows for expansion or…
The present paper aims to investigate the metric mean dimension theory of continuous flows. We introduce the notion of metric mean dimension for continuous flows to characterize the complexity of flows with infinite topological entropy. For…
Recently, a combinatorial interpretation of Baldoni and Vergne's generalized Lidskii formula for the volume of a flow polytope was developed by Benedetti et al.. This converts the problem of computing Kostant partition functions into a…
Maxwell models for viscoelastic flows are famous for their potential to unify elastic motions of solids with viscous motions of liquids in the continuum mechanics perspective. But the usual Maxwell models allow one to define well motions…
The paper deals with a theoretical study of electrokinetic flow of a rheological Herschel-Bulkley fluid through a cylindrical tube of variable cross-section. The concern of this study is to analyze combined pressure-driven and…
It is well known that Kasner-type cosmologies provide a useful framework for analyzing the three-dimensional anisotropic expansion because of the simplification of the anisotropic dynamics. In this paper relativistic multi-fluid Kasner-type…
Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence…
The abstract hyperbolic sets are introduced. Continuous and differentiable mappings as well as rate of convergence and transversal manifolds are not under discussion, and the symbolic dynamics paradigm is realized in a new way. Our…
Normal geodesic flows flows of Carnot-Caratheodory are discussed from the point of view of the theory of Hamiltonian systems. The geodesic flows corresponding to left-invariant metrics and left- and -right-invariant rank 2 distributions on…