Indices of fixed points not accumulated by periodic points

We prove that for every integer sequence $I$ satisfying Dold relations there exists a map $f : \mathbb{R}^d \to \mathbb{R}^d$, $d \ge 2$, such that $\mathrm{Per(f)} = \mathrm{Fix(f)} = \{o\}$, where $o$ denotes the origin, and $(i(f^n, o))_n = I$.Comment: 11 pages, 2 figures. Final version to appear in Topol. Methods Nonlinear Ana

Sobre la dinámica de homeomorfismos en torno a puntos fijos en dimensión baja

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, Departamento de Geometría y Topología, leída el 30-09-2013En esta Tesis Doctoral se han estudiado dos problemas de dinámica topológica. En el primer capítulo se examina la dinámica generada por homeomorfismos del plano que conservan orientación, son disipativos y tienen un punto fijo atractivo con región de atracción U no acotada. Se analiza el caso en que el número de rotación asignado al atractor es irracional. En el segundo capítulo se estudia el índice de punto fijo para puntos fijos aislados como conjuntos invariantes para homeomorfismos que invierten orientación en R^3. Se consigue probar que dicho índice es siempre menor o igual que 1. Para la demostración se obtienen resultados sobre índice homológico de Conley discreto, del que se da una descripción completa en dimensión 1 y se aporta una nueva aproximación junto con una nueva prueba de su dualidad. Además, se caracteriza completamente las sucesiones de índices de punto en el caso anteriormente citado y también para el caso de puntos fijos no repulsores de aplicaciones continuas en el plano. In this PhD. Thesis we have studied two problems from topological dynamics. In the first chapter we study the dynamics generated by orientation-preserving planar homeomorphisms which are dissipative and have an attracting fixed point with unbounded basin of attraction U. The case in which the rotation number assigned to the attractor is irrational is studied. In the second chapter we study the fixed point index of fixed points isolated as invariant sets for orientation-reversing homeomorphisms in R^3. It is proved that the index is always less than or equal to 1. Some results about homological discrete Conley index are obtained towards the proof: a complete description in dimension 1 and a new approach together with a new proof of its duality. Furthermore, a complete characterization of the fixed point index sequence in the aforementioned case is provided, and also for the case of non-repelling fixed points for continuous maps in the planeDepto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEunpu

Consciousness, Meaning and the Future Phenomenology

Phenomenological states are generally considered sources of intrinsic motivation for autonomous biological agents. In this paper we will address the issue of exploiting these states for robust goal-directed systems. We will provide an analysis of consciousness in terms of a precise definition of how an agent “understands” the informational flows entering the agent. This model of consciousness and understanding is based in the analysis and evaluation of phenomenological states along potential trajectories in the phase space of the agents. This implies that a possible strategy to follow in order to build autonomous but useful systems is to embed them with the particular, ad-hoc phenomenology that captures the requirements that define the system usefulness from a requirements-strict engineering viewpoint

On the growth rate inequality for self-maps of the sphere

Let $S^m = \{x_0^2 + x_1^2 + \cdots + x_m^2 = 1\}$ and $P = \{x_0 = x_1 = 0\} \cap S^m$. Suppose that $f$ is a self--map of $S^m$ such that $f^{-1}(P) = P$ and $|\mathrm{deg}(f_{|P})| < |\mathrm{deg}(f)|$. Then, the number of fixed points of $f^n$ grows at least exponentially with base $|d| > 1$, where $d = \mathrm{deg}(f)/\mathrm{deg}(f_{|P}) \in \mathbb Z$.Comment: 10 pages, 1 figur

Del mapa al drone: paisajes contemporáneos, nuevas interpretaciones del territorio

[EN] For approximately 4000 years they come realizing graphical images that represent concrete territories those that we are called maps. These geographical representations have been decisive for the appearance of the idea of landscape. From the second half of the 16th century, they are the painters those who orientate his look towards the territory thanks to the creation of these images or maps on the part of the geographers and cartographers. Neither during the forefronts, nor the dadaístas nor surrealistic his actions manage to move to a few cartographic bases and, in addition, they flee of the representations by means of the literary descriptions. For your part, the situacionistas realize maps psicogeográficos, but without the intention of representing the royal paths of his drifts. It is not up to the decade of the years From the second half of the 16th century, they are the painters those who orientate his look towards the territory thanks to the creation of these images or maps on the part of the geographers and cartographers. Neither during the forefronts, nor the dadaístas nor surrealistic his actions manage to move to a few cartographic bases and, in addition, they flee of the representations by means of the literary descriptions. For your part, the situacionistas realize maps psicogeográficos, but without the intention of representing the royal paths of his drifts. It is not up to the decade of the 60s, when some artists like Smithson, Long or Fulton, they decide to confront the world of the art with the problem of the representation and knowledge of the territory, for what they resort to the use of maps as expressive instruments. At present, the new technologies allow to travel all over the world from a computer connected to Internet: there can be explored the places that are wanted, give a virtual or enclosed walk to indicate a place as visited. The cartographic contemporary methods include satellites, supercomputers, flying not crewed devices or chambers capable of catching images of 360 degrees. The object of this article is, on the one hand, to analyze the evolution of the different artistic attitudes opposite to the representation of the territory by means of the use of maps and other cartographic digital devices. And, for other one, to reveal how the virtual methods of knowledge of the territory have transformed the way that looks at the contemporary artist and faces the landscape. This way, modified the point of view, the landscape loses his inertia and the artistic creation is opened towards completely new ways of conceiving his relations with the natural way.[ES] Desde hace unos 4000 años se vienen realizando imágenes gráficas que representan territorios concretos a las que llamamos mapas. Estas representaciones geográficas han sido decisivas para la aparición de la idea de paisaje. A partir de la segunda mitad del siglo XVI, son los pintores los que orientan su mirada hacia el territorio gracias a la creación de estas imágenes o mapas por parte de los geógrafos y cartógrafos. Durante las vanguardias, ni los dadaístas ni los surrealistas llegan a trasladar sus acciones a unas bases cartográficas y, además, huyen de las representaciones mediante las descripciones literarias. Por su parte, los situacionistas realizan mapas psicogeográficos, pero sin la intención de representar las trayectorias reales de sus derivas. No es hasta la década de los años 60, cuando algunos artistas como Smithson, Long o Fulton, deciden confrontar el mundo del arte con el problema de la representación y conocimiento del territorio, por lo que recurren al uso de mapas como instrumentos expresivos. En la actualidad, las nuevas tecnologías permiten viajar por todo el mundo desde un ordenador conectado a Internet: se pueden explorar los lugares que se quiera, dar un paseo virtual o incluso señalar un lugar como visitado. Los métodos cartográficos contemporáneos incluyen satélites, superordenadores, aparatos voladores no tripulados o cámaras capaces de captar imágenes de 360 grados.El objeto de este artículo es, por un lado, analizar la evolución de las distintas actitudes artísticas frente a la representación del territorio mediante el uso de mapas y otros dispositivos cartográficos digitales. Y, por otro, desvelar cómo los métodos de conocimiento virtuales del territorio han transformado la manera en que al artista contemporáneo mira y se enfrenta al paisaje. Así, modificado el punto de vista, el paisaje pierde su inercia y la creación artística se abre hacia formas completamente nuevas de concebir sus relaciones con el medio natural.Corbato, R. (2015). Del mapa al drone: paisajes contemporáneos, nuevas interpretaciones del territorio. En II CONGRESO INTERNACIONAL DE INVESTIGACIÓN EN ARTE VISUALES. Editorial Universitat Politècnica de València. 196-202. https://doi.org/10.4995/ANIAV2015.1261OCS19620

La importancia del lugar en la obra de Carlos Rodríguez-Méndez

This article examines the importance of place in the work of Spanish artist Carlos Rodríguez-Méndez, through four of his works. The relationship between the place of the work, the material and the concept of home is studied, as well as his processual way of understanding the sculptural practice, to verify that belonging is one of the main objectives of his workinfo:eu-repo/semantics/publishedVersio

Gravity Survey of the Serpent Mound Area, Southern Ohio

Author Institution: Department of Geology, The Ohio State University, Columbus, Ohio 43210Over most of south-central Ohio, the sedimentary Paleozoic rocks exposed at the surface are relatively flat-lying, but in the Serpent Mound area of Highland and Adams Counties they show a circular feature, four miles in diameter, in which the rocks are complexly faulted. This structure has not yet been satisfactorily explained; two of the hypotheses proposed to explain its origin are 1) that it was caused by a "cryptovolcanic" event and 2) that it is an "astrobleme," produced by the impact of a meteoritic body. These two possible mechanisms might be distinguished by the attendant differences in the density variations produced: the cryptovolcanic structure could be associated with large lateral variations in density at the level of the basement rocks, while the meteoritic impact could produce shatter zones and brecciated layers, and small reductions in density in the rock lying closer to the surface. A closely-spaced network of gravity stations extending beyond the limits of the surface expression of the ring structure shows no gravity anomaly pattern that can be related to the surface features. Supporters of the astrobleme hypothesis are more likely to find this evidence useful than are the cryptovolcanists