Related papers: Generating Forms for Exact Volume-Preserving Maps

In this article we introduce a new method for constructing implicit symplectic maps using special symplectic manifolds and Liouvillian forms. This method extends, in a natural way, the method of generating functions to 1-forms which are…

We study quadratic, volume preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the H\'enon area preserving map and the family of symplectic quadratic maps studied by Moser. In particular, we investigate a family…

We study exact, volume-preserving diffeomorphisms that have heteroclinic connections between a pair of normally hyperbolic invariant manifolds. We develop a general theory of lobes, showing that the lobe volume is given by an integral of a…

We study quadratic, volume preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the Henon area preserving map and the family of symplectic quadratic maps studied by Moser. In particular, we investigate a family…

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 construct examples of volume-preserving uniquely ergodic (and hence minimal) real-analytic diffeomorphisms on odd-dimemsional spheres

In this letter, we present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M, \omega). It is shown that every volume-preserving flow has some 2-forms acting the role of the Hamiltonian…

We use cotangent bundles of spaces of smooth embeddings to construct symplectic dual pairs involving the group of volume preserving diffeomorphisms. Via symplectic reduction we obtain descriptions of coadjoint orbits of this group in terms…

We determine the Riemannian manifolds for which the group of exact volume preserving diffeomorphisms is a totally geodesic subgroup of the group of volume preserving diffeomorphisms, considering right invariant $L^2$-metrics. The same is…

We study diffeomorphisms that have one-parameter families of continuous symmetries. For general maps, in contrast to the symplectic case, existence of a symmetry no longer implies existence of an invariant. Conversely, a map with an…

In earlier work, Lomeli and Meiss used a generalization of the symplectic approach to study volume preserving generating differential forms. In particular, for the $\mathbb{R}^3$ case, the first to differ from the symplectic case, they…

We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is…

We briefly introduce the conception on Euler-Lagrange cohomology groups on a symplectic manifold $(\mathcal{M}^{2n}, \omega)$ and systematically present the general form of volume-preserving equations on the manifold from the cohomological…

This paper meticulously revisit and study the flux geometry of any compact oriented manifold $(M; W)$. We generalize several well-known factorization results, exhibit some orbital conditions for the study of flux geometry, give a proof of…

A theorem of Moser guarantees that every diffeomorphism of a closed manifold can be isotoped to a volume preserving one. We show that this statement cannot be extended into contact category: some connected components of contactomorphism…

We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected)…

We study the flux homomorphism for closed forms of arbitrary degree, with special emphasis on volume forms and on symplectic forms. The volume flux group is an invariant of the underlying manifold, whose non-vanishing implies that the…

Suppose M is a noncompact connected oriented C^infty n-manifold and omega is a positive volume form on M. Let D^+(M) denote the group of orientation preserving diffeomorphisms of M endowed with the compact-open C^infty topology and D(M;…

We study the dynamics of the five-parameter quadratic family of volume-preserving diffeomorphisms of R^3. This family is the unfolded normal form for a bifurcation of a fixed point with a triple-one multiplier and also is the general form…

I construct the real counterparts (which I call Borel-Bott classes) of the R/Z classes constructed in "Characteristic classes in symplectic topology", to appear, in the cohomology of volume-preserving and symplectomorhisms of a compact…