Quantum relativistic cosmology: Dynamical interpretation and tunneling universe

In this work, the wave functions associated to the quantum relativistic universe, which is described by the Wheeler–DeWitt equation, are obtained. Taking into account different kinds of energy density, namely, matter, radiation, vacuum, dark energy and quintessence, we discuss some aspects of the quantum dynamics. In all these cases, the wave functions of the quantum relativistic universe are given in terms of the triconfluent Heun functions. We investigate the expansion of the universe using these solutions and found that the asymptotic behavior for the scale factor is [Formula: see text] for whatever the form of energy density is. On the other hand, we analyze the behavior at early stages of the universe and found that [Formula: see text]. We also calculate and analyze the transmission coefficient through the effective potential barrier.

A local study near the Wolff point on the ball

Let f be a holomorphic self-map of the unit ball in dimension 2, which does not have an interior fixed point. Suppose that f has a Wolff point p with the boundary dilatation coefficient equal to 1 and the non-tangential differential dfp = id. The local behaviours of f near p are quite diverse, and we give a detailed study in many typical cases. As a byproduct, we give a dynamical interpretation of the Burns–Krantz rigidity theorem. Note also that similar results hold on two-dimensional contractible smoothly bounded strongly pseudoconvex domains.

On Baire measurable colorings of group actions

The field of descriptive combinatorics investigates to what extent classical combinatorial results and techniques can be made topologically or measure-theoretically well behaved. This paper examines a class of coloring problems induced by actions of countable groups on Polish spaces, with the requirement that the desired coloring be Baire measurable. We show that the set of all such coloring problems that admit a Baire measurable solution for a particular free action $\unicode[STIX]{x1D6FC}$ is complete analytic (apart from the trivial situation when the orbit equivalence relation induced by $\unicode[STIX]{x1D6FC}$ is smooth on a comeager set); this result confirms the ‘hardness’ of finding a topologically well-behaved coloring. When $\unicode[STIX]{x1D6FC}$ is the shift action, we characterize the class of problems for which $\unicode[STIX]{x1D6FC}$ has a Baire measurable coloring in purely combinatorial terms; it turns out that closely related concepts have already been studied in graph theory with no relation to descriptive set theory. We remark that our framework permits a wholly dynamical interpretation (with colorings corresponding to equivariant maps to a given subshift), so this article can also be viewed as a contribution to generic dynamics.

Shear properties of Earth’s inner core constrained by a detection ofJwaves in global correlation wavefield

SeismicJwaves, shear waves that traverse Earth’s inner core, provide direct constraints on the inner core’s solidity and shear properties. However, these waves have been elusive in the direct seismic wavefield because of their small amplitudes. We devised a new method to detectJwaves in the earthquake coda correlation wavefield. They manifest through the similarity with other compressional core-sensitive signals. The inner core is solid, but relatively soft, with shear-wave speeds and shear moduli of 3.42 ± 0.02 kilometers per second and 149.0 ± 1.6 gigapascals (GPa) near the inner core boundary and 3.58 ± 0.02 kilometers per second and 167.4 ± 1.6 GPa in Earth’s center. The values are 2.5% lower than the widely used Preliminary Earth Reference Model. This provides new constraints on the dynamical interpretation of Earth’s inner core.

Sensorimotor Life

This book elaborates a series of contributions to a non–representational theory of action and perception. It is based on current theoretical developments in the enactive approach to life and mind. These enactive ideas are applied and extended to provide a theoretically rich, naturalistic account of sensorimotor meaning and agency. This account supplies non–representational extensions to the sensorimotor approach to perceptual experience based on the notion of the living body as a self–organizing dynamic system in coupling with the environment. The enactive perspective entails the use of world–involving explanations, in which processes external to an agent co–constitute mental phenomena in ways that cannot be reduced to the supply of information for internal processing. These contributions to sensorimotor theories are a dynamical–systems description of different types of sensorimotor regularities or sensorimotor contingencies, a dynamical interpretation of Piaget's theory of equilibration to ground the concept of sensorimotor mastery, and a theory of agency as organized networks of sensorimotor schemes, with its implications for sensorimotor subjectivity. New tools are provided for examining the organization, development, and operation of networks of sensorimotor schemes that compose regional activities and genres of action with their own situated norms. This permits the exploration of new explanations for the phenomenology of agency experience that are favorably contrasted with traditional computational approaches and lead to new empirical predictions. From these proposals, capabilities once beyond the reach of enactive explanations, such as the possibility of virtual actions and the adoption of socially mediated abstract perceptual attitudes, can be addressed.

Topological entropy in totally disconnected locally compact groups

Let $G$ be a topological group, let $\unicode[STIX]{x1D719}$ be a continuous endomorphism of $G$ and let $H$ be a closed $\unicode[STIX]{x1D719}$-invariant subgroup of $G$. We study whether the topological entropy is an additive invariant, that is, $$\begin{eqnarray}h_{\text{top}}(\unicode[STIX]{x1D719})=h_{\text{top}}(\unicode[STIX]{x1D719}\restriction _{H})+h_{\text{top}}(\bar{\unicode[STIX]{x1D719}}),\end{eqnarray}$$ where $\bar{\unicode[STIX]{x1D719}}:G/H\rightarrow G/H$ is the map induced by $\unicode[STIX]{x1D719}$. We concentrate on the case when $G$ is totally disconnected locally compact and $H$ is either compact or normal. Under these hypotheses, we show that the above additivity property holds true whenever $\unicode[STIX]{x1D719}H=H$ and $\ker (\unicode[STIX]{x1D719})\leq H$. As an application, we give a dynamical interpretation of the scale $s(\unicode[STIX]{x1D719})$ by showing that $\log s(\unicode[STIX]{x1D719})$ is the topological entropy of a suitable map induced by $\unicode[STIX]{x1D719}$. Finally, we give necessary and sufficient conditions for the equality $\log s(\unicode[STIX]{x1D719})=h_{\text{top}}(\unicode[STIX]{x1D719})$ to hold.