A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Characterizes Anosov flows in 3D using symplectic and contact geometry.
Introduces GFC for learning complex dynamical systems with geometric constraints.
Characterizes Anosov flows via contact geometry.
Bi-contact surgery operations can be applied to Anosov flows.
We provide obstructions to the existence of conformally Anosov Reeb flows on a 3-manifold that partially generalize similar obstructions to Anosov Reeb flows. In particular, we show does not admit conformally Anosov Reeb flows. We also give a Riemannian geometric condition on a metric compatible with a c…
We prove that every non-degenerate Reeb flow on a closed contact manifold admitting a strong symplectic filling with vanishing first Chern class carries at least two geometrically distinct closed orbits provided that the positive equivariant symplectic homology of satisfies a mild condition. Under further a…
New abelian cohomology theory applied to rigidity of flows.
Geometric flow on curves in S^3 generates YO equations solutions.
Study develops curvature for contact-sequence networks, revealing temporal dynamics.
Study vector fields on hyperbolic spaces to create Ricci-Bourguignon solitons.
This is a personal view of some problems on minimal surfaces, Ricci flow, polyhedral geometric structures, Haken 4-manifolds, contact structures and Heegaard splittings, singular incompressible surfaces after the Hamilton-Perelman revolution.
Recent research on accelerated gradient methods of use in optimization has demonstrated that these methods can be derived as discretizations of dynamical systems. This, in turn, has provided a basis for more systematic investigations, especially into the geometric structure of those dynamical systems and their structur…
New contact structures detected by contact homology.
We give a twistorial interpretation of geometric structures on a Riemannian manifold, as sections of homogeneous fibre bundles, following an original insight by Wood (2003). The natural Dirichlet energy induces an abstract harmonicity condition, which gives rise to a geometric gradient flow. We establish a number of an…
In this paper, we classify the three-dimensional contact partially hyperbolic diffeomorphisms whose stable, unstable and central distributions are smooth, and whose non-wandering set equals the whole manifold. We prove that up to a finite quotient or a finite power, they are smoothly conjugated either to the time-one m…
We give a sharp lower bound for the number of geometrically distinct contractible periodic orbits of dynamically convex Reeb flows on prequantizations of symplectic manifolds that are not aspherical. Several consequences of this result are obtained, like a new proof that every bumpy Finsler metric on carries at l…
Generalizes surgery techniques for projectively Anosov flows.
New flow category for contact manifolds from Reeb orbits.
New surgery method preserves Anosov flow properties using bi-contact geometry.
The Euler class conjecture links geometric structures to integral points on the Thurston norm ball.
Invites study of contact structures and Reeb flows dynamics.
3D contact manifolds have optimal higher systolic ratios.
A flow-spine of a 3-manifold is a spine admitting a flow that is transverse to the spine, where the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. We say that a contact structure on a closed, connected, oriented 3-manifold is supported by a flow-spine if it has a contact form w…
We consider evolution equations for curves in the 3-dimensional sphere that are invariant under the group of pseudoconformal transformations, which preserves the standard contact structure on the sphere. In particular, we investigate how invariant evolutions of Legendrian and transverse curves induce we…
We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the quantum Hamiltonian dynamics associated with classical Hamiltonian flows over closed prequantized symplectic manifolds in the context of geometric quantization of Kostant and Souriau. We express the associated evolution operators via paral…
We study the sub-Riemannian exponential for contact distributions on manifolds of dimension greater or equal to 5. We compute an approximation of the sub-Riemannian Hamiltonian flow and show that the conjugate time can have multiplicity 2 in this case. We obtain an approximation of the first conjugate locus for small r…
Entropy rigidity for Finsler flows but collapse for Reeb flows.
The paper proves rigidity results for Anosov flows and their orbit equivalences.
Study proves existence of weak mean curvature flow with contact angle.
Inspired by Katok's examples of Finsler metrics with a small number of closed geodesics, we present two results on Reeb flows with finitely many periodic orbits. The first result is concerned with a contact-geometric description of magnetic flows on the 2-sphere found recently by Benedetti. We give a simple interpretat…
Local normal forms for symmetrical contact structures on 3-manifolds.
This paper proves a map from flow-spines to contact structures is surjective.
Mean curvature flow converges to a translating soliton with prescribed contact angle.
The study finds many tight contact structures on hyperbolic 3-spheres.
We prove that a topological contact isotopy uniquely defines a topological contact Hamiltonian. Combined with previous results from [MS11], this generalizes the classical one-to-one correspondence between smooth contact isotopies and their generating smooth contact Hamiltonians and conformal factors to the group of top…
The paper generalizes rigidity results for contact Anosov flows with bunching assumption.
We introduce a new object, the dynamical torsion, which extends the potentially ill-defined value at of the Ruelle zeta function of a contact Anosov flow twisted by an acyclic representation of the fundamental group. We show important properties of the dynamical torsion: it is invariant under deformations among con…
Study geometric structures on twistor and reflector spaces of paraquaternionic contact manifolds.
We introduce the notion of contact Ricci flow associated with the Reeb vector field. Using it, we give a simple proof of the Poincare conjecture.
Paper proves minimizing movements match smooth droplet flow in 3D.
Study on flows of G2-structures on contact Calabi-Yau 7-manifolds.
Study gradient flow of phase transitions with fixed contact angle.
Study shows magnetic trajectories in Berger spheres are homogeneous.
Study eta invariant remainder on contact manifolds, improving previous results.
These are notes based on a mini-course at the conference RIEMain in Contact, held in Cagliari, Sardinia, in June 2018. The main theme is the connection between Reeb dynamics and topology. Topics discussed include traps for Reeb flows, plugs for Hamiltonian flows, the Weinstein conjecture, Reeb flows with finite numbers…
These notes are intended to be an introduction to the use of approximately holomorphic techniques in almost contact and contact geometry. We develop the setup of the approximately holomorphic geometry. Once done, we sketch the existence of the two main geometric decompositions available for an almost contact or contact…
Tichler proved that a manifold admitting a smooth closed one-form fibers over a circle. More generally a manifold admitting independent closed one-forms fibers over a torus . In this article we explain a version of this construction for manifolds with boundary using the techniques of -calculus. We explore n…
We prove exponential decay of correlations for Hölder continuous observables with respect to any Gibbs measure for contact Anosov flows admitting Pesin sets with exponentially small tails. This is achieved by establishing strong spectral estimates for certain Ruelle transfer operators for such flows.