Related papers: Real Polynomial Diffeomorphisms with Maximal Entro…
In work the internal structure of de Rham cohomology is considered. As examples the phase flows in $\mathbb {R}^3$ admitting the Nambu Poisson structure are studied.
We study graph complexes related to configuration spaces and diffeomorphism groups of highly connected manifolds of odd dimension. In particular we compute the cohomology in the "high genus" limit. This paper is a continuation of previous…
We consider general Morse-Smale diffeomorphisms on a closed orientable two-dimentional surface. In this paper it is proved that the complete topological invariant of Morse-Smale diffeomorphisms is finite, the algorithm of the construction…
The emphasis of this course is on pluripotential methods in complex dynamics in higher dimension. They are based on the compactness properties of plurisubharmonic functions and on the theory of positive closed currents. Applications of…
The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD, viz. models that incorporate two-fluid effects (the Hall term and electron inertia).…
We use the Hopf mapping to construct a magnetic configuration consisting of closed field lines, each of which is linked with all the other ones. We obtain in this way a solution of the equations of magnetohydrodynamics of an ideal…
In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…
We realize several combinatorial Hopf algebras based on set compositions, plane trees and segmented compositions in terms of noncommutative polynomials in infinitely many variables. For each of them, we describe a trialgebra structure, an…
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
In this note we construct measures of maximal entropy for a certain class of maps with critical points called Viana maps. The main ingredients of the proof are the non-uniform expansion features and the slow recurrence (to the critical set)…
In this paper, we derive a simple method for separating topological noise from topological features using a novel measure for comparing persistence barcodes called persistent entropy.
We study the topological persistence of the (path) configuration spaces and the (path) independence complexes for digraphs as well as their underlying graphs. We construct some canonical embeddings from the (path) independence complexes of…
In this paper, we investigate the topology of a class of non-K\"ahler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics in $\Bbb C^n$…
Given a topological cell decomposition of a closed surface equipped with edge weights, we consider the Dirichlet energy of any geodesic realization of the 1-skeleton graph to a hyperbolic surface. By minimizing the energy over all possible…
The Maximum Entropy Principle (MEP) is a method that can be used to infer the value of an unknown quantity in a set of probability functions. In this work we review two applications of MEP: one giving a precise inference of the Higgs boson…
Let $X$ be a compact complex manifold of dimension $k$ and $f:X \longrightarrow X$ be a dominating meromorphic map. We generalize the notion of topological entropy, by defining a quantity $h_{(m,l)}^{top}(f)$ which measures the action of…
We prove that any diffeomorphism of a compact manifold can be C^1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a diffeomorphism which is partially…
For an expansive homeomorphism, we investigate the relationship among dimension, entropy, and Lyapunov exponents. Motivated by Young's formula for surface diffeomorphisms, which links dimension and measure-theoretic entropy with hyperbolic…
The local multiplicities of the Maxwell sets in the spaces of versal deformations of Pham holomorphic function singularities are calculated. A similar calculation for some other bifurcation sets (generalized Stokes' sets) defined by more…
We present a new methodology for the characterization of the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. This procedure does not rely on the explicit construction of coverings or packings and…