Related papers: Monotone flows with dense periodic orbits
We provide sufficient conditions on a positive function so that its associated special flow over any irrational rotation is either weak mixing or $L^2$-conjugate to a suspension flow.
Pointwise zero velocity helicity density is shown not to prevent steady flows from acting as kinematic dynamos. We present numerical evidences that such flows can generate both small-scale magnetic fields as well as, by the magnetic…
The main result of this work is the following: for volume preserving flows on compact manifolds with the $C^r$ topology, $1 \leqq r \leqq \infty$ , the closure of every invariant manifold of periodic orbits and singularities is a chain…
We prove that, whenever $G$ is a Polish group with metrizable universal minimal flow $M(G)$, there exists a comeagre orbit in $M(G)$. It then follows that there exists an extremely amenable, closed, coprecompact $G^*$ of $G$ such that $M(G)…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
We show that the existence of one simple closed Reeb orbit of a particular type (a symplectically degenerate maximum) forces the Reeb flow to have infinitely many periodic orbits. We use this result to give a different proof of a recent…
Moir\'e patterns are omnipresent. They are important for any overlapping periodic phenomenon, from vibrational and electromagnetic, to condensed matter. Here we show, both theoretically and via experimental simulations by ultracold atoms,…
Periodic geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle $\mathrm{PSL}_2(\mathbb{Z})\backslash\mathrm{PSL}_2(\mathbb{R})$. The complement of any finite number of orbits is a…
We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes (i.e., periodic orbits) near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium…
The existence of smooth periodic traveling solutions in the Dullin-Gottwald-Holm (DGH) equation and the monotonicity of the period function are clarified. By introducing two suitable parameters, we show the existence of periodic travelling…
Surfaces admitting flows all whose orbits are dense are called minimal. Minimal orientable surfaces were characterized by J.C. Beni\`{e}re in 1998, leaving open the nonorientable case. This paper fills this gap providing a characterization…
For each $n\in\mathbb{Z}^+$, we show the existence of Venice masks (i.e. intransitive sectional-Anosov flows with dense periodic orbits) containing $n$ equilibria on certain compact 3-manifolds. These examples are characterized because of…
We show existence of relative periodic orbits (a.k.a. relative nonlinear normal modes) near relative equilibria of a symmetric Hamiltonian system under an appropriate assumption on the Hessian of the Hamiltonian. This gives a relative…
Given a possibly discontinuous, bounded function $f:\mathbb{R}\mapsto\mathbb{R}$, we consider the set of generalized flows, obtained by assigning a probability measure on the set of Carath\'eodory solutions to the ODE ~$\dot x = f(x)$. The…
We showed earlier that the level set function of a monotonic advancing front is twice differentiable everywhere with bounded second derivative. We show here that the second derivative is continuous if and only if the flow has a single…
A continuum $X$ is a dendrite if it is locally connected and contains no simple closed curve, a self mapping $f$ of $X$ is called monotone if the preimage of any connected subset of $X$ is connected. If $X$ is a dendrite and $f:X\to X$ is a…
We consider the long-time behavior of the mean curvature flow in heterogeneous media with periodic fibrations, modeled as an additive driving force. Under appropriate assumptions on the forcing term, we show existence of generalized…
We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With the goal of providing a complete self-contained proof,…
Fluid cosmologies are consistent with the generally accepted observational evidence during intermediate and late times, and they need not have singular behavior in primordial times. A general form for fluid cosmology consistent with…
We develop a monotone finite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that the convergence rate of this method is order 1 in space and if the space grid…