Related papers: Slow area-preserving diffeomorphisms of the torus
We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism $f$ on a closed $3$-manifold with exponential growth in its fundamental group such that $f^n$ is not isotopic to the identity for all $n\neq…
For a nonlinear Anosov diffeomorphism of the 2-torus, we present examples of measures so that the group of $\mu$-preserving diffeomorphisms is, up to zero-entropy transformations, cyclic. For families of equilibrium states $\mu$, we…
We address the problem about under what conditions an endomorphism having a dense orbit, verifies that a sufficiently close perturbed map also exhibits a dense orbit. In this direction, we give sufficient conditions, that cover a large…
We present two constructions, both inspired by ideas from graph theory, of sequences random surfaces of growing area, whose systoles grow logarithmically as a function of their area. This also allows us to prove a new lower bound on the…
This contribution is the first in a series of three: it reports on the construction of (a fine sheaf of) diffeomorphism invariant Colombeau algebras on open sets of Eucildean space, which completes earlier approaches. Part II and III will…
We prove that dynamical coherence is an open and closed property in the space of partially hyperbolic diffeomorphisms of $\mathbb{T}^3$ isotopic to Anosov. Moreover, we prove that strong partially hyperbolic diffeomorphisms of…
The first result is the semicontinuity of automorphism groups for the collection of complex two-dimensional bounded pseudoconvex domains with smooth boundary of finite D'Angelo type. The method of proof is new so that it simplifies the…
We present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a wide class of infinite-dimensional dynamical systems with time-scale separation. The framework is applicable to models where an…
We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfoldings and establish results related to the appearance of…
We present an approximation by conjugation scheme to obtain real-analytic diffeomorphisms of odd dimensional spheres that are weakly mixing with respect to the volume.
We study the dynamics of area-preserving maps in a non-compact setting. We show that the $C^{\infty}$-closing lemma holds for area-preserving diffeomorphisms on a closed surface with finitely many points removed. As a corollary, a…
We use numerical and analytical tools to demonstrate arguments in favor of the existence of a family of smooth, symplectic diffeomorphisms of the two-dimensional torus that have both a positive measure set with positive Lyapunov exponent…
In this paper, we study transitive partially hyperbolic diffeomorphisms with one-dimensional topologically neutral center, meaning that the length of the iterate of small center segments remains small. Such systems are dynamically coherent.…
This paper introduces two new abstract morphs for two $2$-dimensional shapes. The intermediate shapes gradually reduce the Hausdorff distance to the goal shape and increase the Hausdorff distance to the initial shape. The morphs are…
This is the second of a series of two papers where we construct embedded Willmore tori with small area constraint in Riemannian three-manifolds. In both papers the construction relies on a Lyapunov-Schmidt reduction, the difficulty being…
Incompressible two-dimensional flows such as the advection (Liouville) equation and the Euler equations have a large family of conservation laws related to conservation of area. We present two Eulerian numerical methods which preserve a…
We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in each component. We show that within this two parameter family of maps,…
A diffeomorphism of pseudo-Riemannian manifolds is called sectional curvature preserving if it preserves the sectional curvature of all the nondegenerate 2-planes. We consider a similar condition for degenerate 2-planes and we prove that…
A conservative irrational pseudo-rotation of the two-torus is semi-conjugate to the irrational rotation if and only if it has the property of bounded mean motion [10]. (Here 'irrational pseudo-rotation' means a toral homeomorphism with…
We consider two natural Lagrangian intersection problems in the context of symplectic toric manifolds: displaceability of torus orbits and of a torus orbit with the real part of the toric manifold. Our remarks address the fact that one can…