Related papers: Robust transitivity for endomorphisms admitting cr…
We provide sufficient conditions for a mapping $f:R^{n}\rightarrow R^{n}$ to be a global diffeomorphism in case it is strictly (Hadamard) differentiable. We use classical local invertibility conditions together with the non-smooth critical…
We prove that every robustly transitive and every stably ergodic symplectic diffeomorphism on a compact manifold admits a dominated splitting. In fact, these diffeomorphisms are partially hyperbolic.
We propose sufficient conditions for existence of topologically stable periodic canard solutions in non-smooth slow-fast systems.
In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real…
In this paper we apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit…
A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
Robustness verification that aims to formally certify the prediction behavior of neural networks has become an important tool for understanding model behavior and obtaining safety guarantees. However, previous methods can usually only…
The energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid's bus angles to retain synchronism after the occurrence of a major fault. In this paper a…
Bipedal locomotion is a phenomenon that still eludes a fundamental and concise mathematical understanding. Conceptual models that capture some relevant aspects of the process exist but their full explanatory power is not yet exhausted. In…
In this paper, we study robust transshipment under consistent flow constraints. We consider demand uncertainty represented by a finite set of scenarios and characterize a subset of arcs as so-called fixed arcs. In each scenario, we require…
We provide sufficient conditions for smooth conjugacy between two Anosov endomorphisms on the 2-torus. From that, we also explore how the regularity of the stable and unstable foliations implies smooth conjugacy inside a class of…
We establish sufficient and necessary conditions for the joint transitivity of linear iterates in a minimal topological dynamical system with commuting transformations. This result provides the first topological analogue of the classical…
We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…
Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the…
In the early 1980's Thurston gave a topological characterization of rational maps whose critical points have finite iterated orbits (\cite{Th,DH1}): given a topological branched covering $F$ of the two sphere with finite critical orbits, if…
We consider a thermodynamically consistent model for the evolution of thermally conducting two-phase incompressible fluids. Complementing previous results, we prove additional regularity properties of solutions in the case when the…
The cohomological rigidity problem for toric orbifolds asks when an integral cohomology isomorphism implies a homotopy equivalence. In this paper we reformulate the cohomological rigidity problem in the context of $4$-dimensional toric…
This paper is devoted to study the topological invariance of several non-uniform hyperbolicity conditions of one-dimensional maps. In contrast with the case of maps with only one critical point, it is known that for maps with several…
In this article, we prove a rigidity criterion for period maps of admissible variations of graded-polarizable mixed Hodge structure, and establish rigidity in a number of cases, including families of quasi-projective curves, projective…