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.
Paper shows leafwise cohomological expression for dynamical zeta functions.
Formula derived for zeta functions of 3D foliated systems.
Since the pioneering work of Ghys, Langevin and Walczak among others, it has been known that several methods of dynamical systems theory can be adopted to study of foliations. Our aim in this paper is to investigate complexity of foliations, by generalising existence problem of time averages in dynamical systems theory…
First, we survey some results on classical and quantum dynamical systems associated with transverse Dirac operators on Riemannian foliations. Then we illustrate these results by two examples of Riemannian foliations: a foliation given by the fibers of a fibration and a linear foliation on the two-dimensional torus.
Foliate systems are those which preserve some (possibly singular) foliation of phase space, such as systems with integrals, systems with continuous symmetries, and skew product systems. We study numerical integrators which also preserve the foliation. The case in which the foliation is given by the orbits of an action …
We discuss analogies between number theory and the theory of dynamical systems on spaces with a one-codimensional foliation. The emphasis is on comparing the "explicit formulas" of analytic number theory with certain dynamical Lefschetz trace formulas. We also point out a possible relation between an Arakelov-Euler cha…
This manuscript is an introduction to the theory of holomorphic foliations on the complex projective plane. Historically the subject has emerged from the theory of ODEs in the complex domain and various attempts to solve Hilbert's 16th Problem, but with the introduction of complex algebraic geometry, foliation theory a…
Develops an oblique projection technique to approximate a foliation for non-normal dynamics.
Anosov flow found in specific partially hyperbolic systems.
This paper simplifies complex nonholonomic systems using momentum map reduction.
We show some fundamental results concerning -dimensional foliated dynamical systems (FDS for short) introduced by Deninger. Firstly, we give a decomposition theorem for an FDS, which yields a classification of FDS's. Secondly, for each type of the classification, we construct concrete examples of FDS…
Study of centralizer elements preserving geodesic flow foliations on covers.
Following Losik's approach to Gelfand's formal geometry, certain characteristic classes for codimension-one foliations coming from the Gelfand-Fuchs cohomology are considered. Sufficient conditions for non-triviality in terms of dynamical properties of generators of the holonomy groups are found. The non-triviality for…
Survey uses Milnor fibrations to classify first integrals of differential systems.
This survey is based on a series of five lectures, given May 3--7, 2010, at the Centre de Recerca Matematica, Barcelona. The goal of the lectures was to present aspects of the theory of foliation dynamical systems which have particular importance for the classification of foliations of compact manifolds. The lectures e…
We study here the action of subgroups of PSL(2,R) on the space of harmonic functions on the unit disc bounded by a common constant, as well as the relationship this action has with the foliated Liouville problem: Given a foliation of a compact manifold by Riemannian leaves and a leafwise harmonic continuous function on…
Let F be a codimension-one, C^2-foliation on a manifold M without boundary. In this work we show that if the Godbillon--Vey class GV(F) \in H^3(M) is non-zero, then F has a hyperbolic resilient leaf. Our approach is based on methods of C^1-dynamical systems, and does not use the classification theory of C^2-foliations.…
We give a survey of the approaches to classifying foliations, starting with the Haefliger classifying spaces and the various results and examples about the secondary classes of foliations. Various dynamical properties of foliations are introduced and discussed, including expansion rate, local entropy, and orbit growth …
Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of singular spaces, orbifolds, stratified spaces... In this work, we prove existence o…
This paper connects foliations of the plane to non-Hausdorff 1-manifolds.
The paper proves regularity of states on manifolds with unstable dynamics.
Study partially hyperbolic diffeomorphisms in 3D, focusing on foliations and dynamics.
Absolutely partially hyperbolic surface endomorphisms have a coherent center foliation.
In this paper we study a Hamiltonian function on the cotangent bundle of the space of Riemannian metrics on a 3-manifold and prove the orbits of the constrained Hamiltonian dynamical system correspond to -manifolds foliated by hypersurfaces diffeomorphic to .
This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with topology. We also present recent examples which introduce a challenge in the classifi…
Subject of present paper is the review of results of authors on foliation theory and applications of foliation theory in control systems. The paper consists of two parts. In the first part the results of authors on foliation theory are presented, in the second part the results on applications of foliation theory in the…
The paper studies stability of discretized Anosov flows.
The paper defines marginal tubes and proves their null nature.
Various problems of geometry, topology and dynamical systems on surfaces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a flat metric with several cone-type singularities. Such flat surfaces are naturally organized into families which appear to b…
Continuity of earthquake flow map transfers Teichmüller dynamics results.
Paper defines dynamical coherence for flows and proves it under specific conditions.
Symmetric Poisson structures linked to geodesic foliations and Jordan algebras.
We consider hyperbolic and partially hyperbolic diffeomorphisms on compact manifolds. Associated with invariant foliation of these systems, we define some topological invariants and show certain relationships between these topological invariants and the geometric and Lyapunov growths of these foliations. As an applicat…
We complete the classification, initiated by the second named author, of homogeneous singular Riemannian foliations of spheres that are lifts of foliations produced from Clifford systems.
A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch provide a subclass of linear involutions. We call such linear involutions non-classical interval exchanges. They are related to measured foliations on orienta…
Constructs initial data leading to apparent horizons and tests Penrose Inequality.
We extend the unpublished work of M. Handel and R. Miller on the classification, up to isotopy, of endperiodic automorphisms of surfaces. We give the Handel-Miller construction of the geodesic laminations, give an axiomatic theory for pseudo-geodesic lamaniations, show the geodesic laminations satisfy the axioms, and p…
Characterizes flag geometries for Hitchin representations in SL3(R).
The main result of the present paper is a coincidence formula for foliated manifolds. To prove this we establish Kuenneth formula, Poincare duality and intersection product in the context of tangential de Rham cohomology and homology of tangential currents. We apply the formula to get a dynamical Lefschetz formula for …
Paper proves trapped surface formation for Einstein-Maxwell-charged scalar field system.
Study shows dynamics of rank 1 orbifolds in flat surfaces.
New maps connect universal circles to ideal sphere for hyperbolic manifolds.
The theory of differential forms began with a discovery of Poincare who found conservation laws of a new type for Hamiltonian systems - The Integral Invariants. Even in the absence of non-trivial integrals of motion, there exist invariant differential forms: a symplectic two-form, or a contact one-form for geodesic flo…
Unified framework recovers and improves classical Brouwer homeomorphism results.
Defines foliation criterion for dense isoperiodic leaves in rank 1 affine orbifolds.
We introduce a dynamical system which we call the AdaBoost flow. The flow is defined by a system of ODEs with control. We show that three algorithms of the AdaBoost family (i) the AdaBoost algorithm of Schapire and Freund (ii) the arc-gv algorithm of Breiman (iii) the confidence rated prediction of Schapire and Singer …
Investigates integrable systems with linear periodic integral for e(3) Lie algebra.
The dynamics of holomorphic 1-forms are studied, showing ergodic foliations and connected spaces.