Related papers: Local inverses of shift maps along orbits of flows

Let $M$ be a manifold equipped (locally) with a pair of complementary foliations. In Catuogno, da Silva and Ruffino (Stoch. Dyn. 2013), it is shown that, up to a stopping time $\tau$, a stochastic flow of local diffeomorphisms $\varphi_t$…

We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…

We study the J-flow on the toric manifolds, through study the transition map between the moment maps induced by two K\"{a}hler metrics, which is a diffeomorphism between polytopes. This is similar to the work of Fang-Lai, under the…

In this paper we provide extensions of the $\lambda$-Lemma (also known as Inclination Lemma) for piecewise smooth vector fields and maps. In order to achieve our main result, we investigate the regularity of time-T-maps of piecewise smooth…

We prove an index theorem concerning the pushforward of flat B-vector bundles, where B is an appropriate algebra. We construct the associated analytic torsion form T. If Z is a smooth closed aspherical manifold, we show that T gives…

This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3-dimensional Anosov flows. We provide a dichotomy result…

Let $\mathcal{F}$ be a foliation with a "singular" submanifold $B$ on a smooth manifold $M$ and $p:E \to B$ be a regular neighborhood of $B$ in $M$. Under certain "homogeneity" assumptions on $\mathcal{F}$ near $B$ we prove that every leaf…

Let $f:R^m \to R$ be a smooth function such that $f(0)=0$. We give a condition on $f$ when for arbitrary preserving orientation diffeomorphism $\phi:\mathbb{R} \to \mathbb{R}$ such that $\phi(0)=0$ the function $\phi\circ f$ is right…

We develop a theory of $\times$-homotopy, fundamental groupoids and covering spaces that apply to non-simple graphs, generalizing existing results for simple graphs. We prove that $\times$-homotopies from finite graphs can be decomposed…

Let $q:M\to M$ be a volume-preserving diffeomorphism of a smooth manifold $M$. We study the possibility to present $q$ as the Poincar\'e map, corresponding to a volume-preserving vector field on $\mathbb{T}\times M$, $\mathbb{T} =…

We consider the time-harmonic electromagnetic transmission problem for the unit sphere. Appealing to a vector spherical harmonics analysis, we prove the first stability result of the local multiple trace formulation (MTF) for…

We prove that a $C^{2+\alpha}$-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class $D_\delta$, $0<\delta<\alpha\le1$, is $C^{1+\alpha-\delta}$-smoothly conjugate to a rigid rotation. We also derive…

The cited article contains a serious flaw. A remedy is found in articles by other authors.

We study the group of volume-preserving diffeomorphisms on a manifold. We develop a general theory of implicit generating forms. Our results generalize the classical formulas for generating functions of symplectic twist maps.

For an orientable surface with an area form, there are two invariants of area-preserving dynamics, the flux homomorphism and the Calabi invariant. Tsuboi found a remarkable connection between the Calabi invariant on the closed disk and a…

In studies of smooth maps with good differential topological conditions such as immersions, embeddings, Morse functions and their higher dimensional versions including fold maps and application to geometry, especially algebraic and…

In this paper we investigate the flow of surfaces by a class of symmetric functions of the principal curvatures with a mixed volume constraint. We consider compact surfaces without boundary that can be written as a graph over a sphere. The…

We introduce new methods in pseudo-isotopy and embedding space theory. As an application we introduce an invariant that detects nontrivial loops of embedded 2-spheres in $S^{2} \times S^{2}$ and in connected sums of $S^{2} \times S^{2}$.…

We classify certain sofic shifts (the irreducible Point Extension Type, or PET, sofic shifts) up to flow equivalence, using invariants of the canonical Fischer cover. There are two main ingredients: (1) An extension theorem, for extending…

This is a survey paper on spaces of automorphisms of manifolds and spaces of manifolds in a fixed homotopy type. It describes the main theorems of traditional surgery theory, but also the main theorems of pseudoisotopy theory, alias…