Related papers: Zero-dimensional and symbolic extensions of topolo…

Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of integrable systems, fluid mechanics, and dynamical systems.…

We introduce the concept of topological expansive flow. We prove that this concept is invariant by topological conjugacy and reduces to expansivity in the compact case. We characterize tiopological expansive flows as rescaling expansive…

In this paper it is proved that near a compact, invariant, proper subset of a continuous flow on a compact, connected metric space, at least one, out of twenty eight relevant dynamical phenomena, will necessarily occur. This result shows…

We extend the concept of expansive measure \cite{am} defined for homeomorphism to flows. We obtain some properties for such measures including abscense of singularities in the support, aperiodicity, expansivity with respect to time-$T$…

We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for…

We study basic properties of flow equivalence on one-dimensional compact metric spaces with a particular emphasis on isotopy in the group of (self-) flow equivalences on such a space. In particular, we show that an orbit-preserving such map…

We establish necessary and sufficient conditions for suspension flows over certain families of shift spaces to be topologically mixing. We also show the similarities and differences between this case and the smooth measure theoretic setting…

We consider volume-preserving flows $(\Phi^f_t)_{t\in\mathbb{R}}$ on $S\times \mathbb{R}$, where $S$ is a closed connected surface of genus $g\geq 2$ and $(\Phi^f_t)_{t\in\mathbb{R}}$ has the form $\Phi^f_t(x,y)=(\phi_tx,y+\int_0^t…

We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…

Planar linear flows are a one-parameter family, with the parameter $\hat{\alpha}\in [-1,1]$ being a measure of the relative magnitudes of extension and vorticity; $\hat{\alpha} = -1$, $0$ and $1$ correspond to solid-body rotation, simple…

We consider linear cocycles taking values in $\textup{SL}_d(\mathbb{R})$ driven by homeomorphic transformations of a smooth manifold, in discrete and continuous time. We show that any discrete-time cocycle can be extended to a…

Euler hydrodynamics of perfect fluids can be viewed as an effective bosonic field theory. In cases when the underlying microscopic system involves Dirac fermions, the quantum anomalies should be properly described. In 1+1 dimensions the…

This paper shows that the topological structures of particle orbits generated by a generic class of vector fields on spherical surfaces, called {\it the flow of finite type}, are in one-to-one correspondence with discrete structures such as…

We show that every volume preserving codimension one Anosov flow on a closed Riemannian manifold of dimension greater than three admits a global cross section and is therefore topologically conjugate to a suspension of a linear toral…

We consider the model of i.i.d. first passage percolation on Z^d, where we associate with the edges of the graph a family of i.i.d. random variables with common distribution G on [0, +$\infty$] (including +$\infty$). Whereas the time…

We present a strategy for a geometric construction of cross sections for the geodesic flow on locally symmetric orbifolds of rank one. We work it out in detail for $\Gamma\backslash H$, where $H$ is the upper half plane and…

We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…

Let $v$ be a continuous flow with arbitrary singularities on a compact surface. Then we show that if $v$ is non-wandering then $v$ is topologically equivalent to a $C^{\infty}$ flow such that there are no exceptional orbits and $\mathrm{P}…

We study dynamics of (anomalous) Galilean superfluid up to first order in derivative expansion, both in parity-even and parity-odd sectors. We construct a relativistic system -- null superfluid, which is a null fluid (introduced in…

We consider the Hamiltonian flow on complex complete intersection surfaces with isolated singularities, equipped with the Jacobian Poisson structure. More generally we consider complete intersections of arbitrary dimension equipped with…