Ergodic theorems for laminations and foliations: recent results and perspectives
From MaRDI portal
Publication:2023888
DOI10.1007/s40306-020-00380-4zbMath1469.37004arXiv2005.07176OpenAlexW3089974560WikidataQ114219378 ScholiaQ114219378MaRDI QIDQ2023888
Publication date: 3 May 2021
Published in: Acta Mathematica Vietnamica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.07176
Lyapunov exponentssingular holomorphic foliationergodic theoremsRiemann surface laminationpositive harmonic currentsleafwise Poincaré metricmultiplicative cocycles
Brownian motion (60J65) Ergodic theorems, spectral theory, Markov operators (37A30) Diffusion processes and stochastic analysis on manifolds (58J65) Foliations in differential topology; geometric theory (57R30) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Transcendental methods of algebraic geometry (complex-analytic aspects) (32J25) Relations between ergodic theory and harmonic analysis (37A46)
Related Items
Poincaré metric of holomorphic foliations with non-degenerate singularities, Directed harmonic currents near non-hyperbolic linearizable singularities, Singular holomorphic foliations by curves. III: Zero Lelong numbers, Heat diffusions on holomorphic foliations with non-degenerate singularities, Singular holomorphic foliations by curves. II: Negative Lyapunov exponent
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Equidistribution of saddle periodic points for Hénon-type automorphisms of \(\mathbb C^k\)
- Limit currents and value distribution of holomorphic maps
- Heat equation and ergodic theorems for Riemann surface laminations
- Lyapunov exponents for surface group representations
- Pfaff systems, currents and hulls
- \(C^ k\)-conjugacy of holomorphic flows near a singularity
- Foliations, the ergodic theorem and Brownian motion
- Examples of minimal laminations and associated currents
- Ergodic properties of rational mappings with large topological degree
- Riemann surface laminations with singularities
- Ergodic theorems. With a supplement by Antoine Brunel
- Quelques problèmes de prolongement de courants en analyse complexe
- On the means of approach to the boundary of Brownian motion
- Gauss-Bonnet theorem for 2-dimensional foliations
- Brownian motion on foliations: Entropy, invariant measures, mixing
- Algebraic solutions of one-dimensional foliations
- Equations de Pfaff algébriques
- Prolongement des courants, positifs, fermes de masse finie
- Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
- Cycles for the dynamical study of foliated manifolds and complex manifolds
- Hypersurfaces solutions d'une équation de Pfaff analytique
- The harmonic measures of Lucy Garnett
- Minimal, rigid foliations by curves on \(\mathbb C\mathbb P^n\)
- Dynamics of polynomial-like mappings
- Lyapunov exponent and the distribution of the periodic points of an endomorphism of \(\mathbb {CP}^k\)
- Diophantine approximations and foliations
- The \(\overline\partial\)-equation on a positive current
- Ergodic theory for Riemann surface laminations: a survey
- Singular holomorphic foliations by curves. I: Integrability of holonomy cocycle in dimension 2
- Super-potentials, densities of currents and number of periodic points for holomorphic maps
- Unique ergodicity for foliations in \(\mathbb {P}^2\) with an invariant curve
- Numerical characterization of the Kähler cone of a compact Kähler manifold
- Minimal sets of foliations on complex projective spaces
- Analyticity of sets associated to Lelong numbers and the extension of closed positive currents
- Some open problems on holomorphic foliation theory
- Geometric characterization of Lyapunov exponents for Riemann surface laminations
- Topology and complex structures of leaves of foliations by Riemann surfaces
- Unique ergodicity of harmonic currents on singular foliations of \({\mathbb{P}^2}\)
- Invariant sets under iteration of rational functions
- Ergodicity of laminations with singularities in Kähler surfaces
- Inexistence of invariant measures for generic rational differential equations in the complex domain
- Random conformal dynamical systems
- Distribution of the values of meromorphic transformations and applications
- Harmonic currents of finite energy and laminations
- [https://portal.mardi4nfdi.de/wiki/Publication:2710399 Uniformization and the Poincar� metric on the leaves of a foliation by curves]
- Equidistribution for meromorphic maps with dominant topological degree
- Entropy for hyperbolic Riemann surface laminations I
- Regularization of currents and entropy
- Hypersurfaces Levi-plates immergées dans les surfaces complexes de courbure positive☆
- Uniformization of surface laminations
- A Synthetic Proof of Makarov's Law of the Iterated Logarithm
- Classifying foliations
- An invariant measure for rational maps
- Proof of the Ergodic Theorem
- Density of positive closed currents, a theory of non-generic intersections
- An Operator Theorem on $L_1$ Convergence to Zero with Applications to Markov Kernels
- Directed harmonic currents near hyperbolic singularities
- Equidistribution problems in complex dynamics of higher dimension
- Statistical behaviour of the leaves of Riccati foliations
- Equilibrium measures of meromorphic self-maps on non-Kähler manifolds
- On the dynamics of Riccati foliations with nonparabolic monodromy representations
- Self-intersection of foliation cycles on complex manifolds
- Dynamics in several complex variables: endomorphisms of projective spaces and polynomial-like mapping
- On closed currents invariant by holomorphic foliations, I
- Two characterizations of equilibrium measure of an endomorphism of \(P^k(\mathbb{C})\)
