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The pentagram map was invented by Richard Schwartz in his search for a projective-geometric analogue of the midpoint map. It turns out that the dynamical behavior of the pentagram map is totally different from that of the midpoint map.…

We propose a set of questions on the dynamics of H\'enon maps from the real, complex, algebraic and arithmetic points of view.

A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as…

We discuss computability and computational complexity of conformal mappings and their boundary extensions. As applications, we review the state of the art regarding computability and complexity of Julia sets, their invariant measures and…

A map from the initial conditions to the values of the function and its first spatial derivative evaluated at the interface is constructed for the heat equation on finite and infinite domains with $n$ interfaces. The existence of this map…

Projectile like fragments emerging from heavy ion collision have an excitation energy which is often labeled by a temperature. This temperature was recently calculated using a geometric model. We expand the geometric model to include also…

We propose a novel witness of temporal quantum entanglement using the imaginary component of the complex heat capacity - a measurable thermodynamic quantity in temperature-modulated calorimetry. By establishing a direct correspondence…

Let f be a rational mapping of a space X . The complexity of (f,X) as a dynamical system is measured by the dynamical degrees $\delta_p(f)$, $1\le p\le {\rm dim}(X)$. We give the definition of the dynamical degrees show how they are…

Traditional two-dimensional risk matrices (heatmaps) are widely used to model and visualize likelihood and impact relationships, but they face fundamental methodological limitations when applied to complex infrastructures. In particular,…

I sketch some pressing questions in several active areas of particle physics and outline the challenges they present for the design and operation of detectors.

The pentagram map, introduced by Schwartz in 1992, is a dynamical system on the moduli space of polygons in the projective plane. Its real and complex dynamics have been explored in detail. We study the pentagram map over an arbitrary…

We present a new dynamical approach for measuring the temperature of a Hamiltonian dynamical system in the micro canonical ensemble of thermodynamics. We show that under the hypothesis of ergodicity the temperature can be computed as a…

In completely local settings, we establish that a dynamically evolving black hole horizon can be assigned a Hawking temperature. Moreover, we calculate the Hawking flux and show that the radius of the horizon shrinks.

Heating plates describe the transfer of heat from actuators to a target object. In other words, they separate the heat sources and heated object and can be further used to apply a specific heat distribution on this object. Therefore, an…

We compute the dynamical degrees of certain compositions of reflections in points on a smooth cubic fourfold. Our interest in these computations stems from the irrationality problem for cubic fourfolds. Namely, we hope that they will…

We study the measurable dynamics of transformations on profinite groups, in particular of those which factor through sufficiently many of the projection maps; these maps generalize the 1-Lipschitz maps on $\mathbb Z_p$.

We show that any birational selfmap of a complex projective surface that has dynamical degree greater than one and is defined over a number field automatically satisfies the Bedford-Diller energy condition after a suitable birational…

We study the equivariant harmonic map heat flow, Schr\"odinger maps equation, and generalized Landau-Lifshitz equation from $\mathbb{C}^n$ to $\mathbb{C}\mathbb{P}^n$. By means of a careful geometric analysis, we determine a new, highly…

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary…

Under the assumption of positive multiplicity, we obtain basic estimates of the hypergeometric functions F\_\la and G\_\la of Heckman and Opdam, and sharp estimates of the particular functions F\_0 and G\_0. Next we prove the Paley-Wiener…