相关论文: Dynamics on Trees of Spheres

We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…

We describe an explicit morphism of complexes that induces the cycle-class maps from (simplicially described) higher Chow groups to rational Deligne cohomology. The reciprocity laws satisfied by the currents we introduce for this purpose…

This work presents a step towards utilizing incrementally-improving symbolic perception knowledge of the robot's surroundings for provably correct reactive control synthesis applied to an autonomous driving problem. Combining abstract…

The dynamic analysis of structural change in the organization of the sciences requires methodologically the integration of multivariate and time-series analysis. Structural change--e.g., interdisciplinary development--is often an objective…

As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters,…

This paper attempts to make feasible the evolutionary emergence of novelty in a supposedly deterministic world which behavior is associated with those of the mathematical dynamical systems. The work was motivated by the observation of…

We study the dynamic scaling hypothesis in invariant surface growth. We show that the existence of power-law scaling of the correlation functions (scale invariance) does not determine a unique dynamic scaling form of the correlation…

Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…

Stabbing queries in sets of intervals are usually answered using segment trees. A dynamic variant of segment trees has been presented by van Kreveld and Overmars, which uses red-black trees to do rebalancing operations. This paper presents…

Suppose that $f \colon X \dashrightarrow X$ is a dominant rational self-map of a smooth projective variety defined over ${\overline{\mathbf Q}}$. Kawaguchi and Silverman conjectured that if $P \in X({\overline{\mathbf Q}})$ is a point with…

The Sullivan dictionary between Kleinian groups and rational dynamics describes striking similarities between the fields, both in terms of the objects of study as well as the techniques used. We give an expository account of a recent bridge…

This article applies the technical framework developed in previous work by the author to discrete admissible covers and their moduli spaces. More precisely, we construct a poic-space that parameterizes the discrete admissible covers after…

We study the boundary behavior of the so-called ring $Q$-mappings obtained as a natural generalization of mappings with bounded distortion. We establish a series of conditions imposed on a function $Q(x)$ for the continuous extension of…

We consider the space of degree $n\ge 2$ rational maps of the Riemann sphere with $k$ distinct marked periodic orbits of given periods. First, we show that this space is irreducible. For $k=2n-2$ and with some mild restrictions on the…

We show that the dynamical degree of an (i.i.d) random sequence of dominant, rational self-maps on projective space is almost surely constant. We then apply this result to height growth and height counting problems in random orbits.

Exact string solutions are presented, where moduli fields are varying with time. They provide examples where a dynamical change of the topology of space is occurring. Some other solutions give cosmological examples where some dimensions are…

This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…

We study the space of linear difference equations with periodic coefficients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations…

We give a 'recursive' formula (in terms of reducible limits) for counting rational curves on a variety moving in any sufficiently large and well-behaved family. Our approach is completely elementary and makes no use of moduli spaces for…

Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be…