相关论文: Real Polynomial Diffeomorphisms with Maximal Entro…
We consider the topology optimization problem of a 2d permanent magnet synchronous machine in magnetostatic operation with demagnetization. This amounts to a PDE-constrained multi-material design optimization problem with an additional…
We determine the homeomorphism type of the set of real points of a smooth projective toric surface. This note may serve as an expository introduction to some of the ideas and techniques in C. Delaunay's work on real toric varieties.
We consider an abundant class of non-uniformly hyperbolic $C^2$-H\'enon like diffeomorphisms called strongly regular and which corresponds to Benedicks-Carleson parameters. We prove the existence of $m>0$ such that for any such…
We show that a $C^1-$generic non partially hyperbolic symplectic diffeomorphism $f$ has topological entropy equal to the supremum of the sum of the positive Lyapunov exponents of its hyperbolic periodic points. Moreover, we also prove that…
Topological entropy is a measure of complex dynamics. In this regard, multimodal maps play an important role when it comes to study low-dimensional chaotic dynamics or explain some features of higher dimensional complex dynamics with…
Let $E$ be a finite-dimensional real vector space and $M\subseteq E$ be a convex polytope with non-empty interior. We turn the group of all $C^\infty$-diffeomorphisms of $M$ into a regular Lie group.
It is known that transitive Anosov diffeomorphisms have a unique measure of maximal entropy (MME). Here we discuss the converse question. Under suitable hypothesis on Lyapunov exponents on the set of periodic points and the structure of the…
We give an upper bound for the topological entropy of maps on inverse limit spaces in terms of their set-valued components. In a special case of a diagonal map on the inverse limit space $\underleftarrow{\lim}(I,f)$, where every diagonal…
We investigate Ruelle-Pollicott resonances of Anosov diffeomorphisms with respect to the measure of maximal entropy. We highlight a profound connection between resonances and eigenvalues of the action induced by the dynamics on de Rham…
To calculate the entropy of a subalgebra or of a channel with respect to a state, one has to solve an intriguing optimalization problem. The latter is also the key part in the entanglement of formation concept, in which case the subalgebra…
We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the…
In Monte Carlo simulation, lattice field theory with a $\theta$ term suffers from the sign problem. This problem can be circumvented by Fourier-transforming the topological charge distribution $P(Q)$. Although this strategy works well for…
Reconstructing 4D or 6D phase space distributions from 1D or 2D measurements is a challenging inverse problem encountered in particle accelerators. Entropy maximization is an established method to incorporate prior information in the…
We extend the notion of the geometric entropy of foliation to foliated manifolds equipped with leafwise Finsler structure. We study the relation between the geometric entropy and the topological entropy of the holonomy pseudogroup. The case…
We prove a theorem of uppersemicontinuity for the metric entropy of meromorphic maps.
We explore the use of the method of Maximum Entropy (ME) as a technique to generate approximations. In a first use of the ME method the "exact" canonical probability distribution of a fluid is approximated by that of a fluid of hard…
We study a germ of real analytic n-dimensional submanifold of $C^n$ that has a complex tangent space of maximal dimension at a CR singularity. Under the condition that its complexification admits the maximum number of deck transformations,…
We show that the variation of the topology at infinity of a two-variable polynomial function is localisable at a finite number of "atypical points" at infinity. We construct an effective algorithm with low complexity in order to detect…
Let f be a meromorphic correspondence on a compact Kahler manifold. We show that the topological entropy of f is bounded from above by the logarithm of its maximal dynamical degree. An analogous estimate for the entropy on subvarieties is…
The goal of this paper is to study the theory of last multipliers in the framework of complex manifolds with a fixed holomorphic volume form. The motivation of our study is based on the equivalence between a holomorphic ODE system and an…