Scaling of the Critical Function for the Standard Map: Some Numerical Results

The behavior of the critical function for the breakdown of the homotopically non-trivial invariant (KAM) curves for the standard map, as the rotation number tends to a rational number, is investigated using a version of Greene's residue criterion. The results are compared to the analogous ones for the radius of convergence of the Lindstedt series, in which case rigorous theorems have been proved. The conjectured interpolation of the critical function in terms of the Bryuno function is discussed.Comment: 26 pages, 3 figures, 13 table

Greene's Residue Criterion for the Breakup of Invariant Tori of Volume-Preserving Maps

Invariant tori play a fundamental role in the dynamics of symplectic and volume-preserving maps. Codimension-one tori are particularly important as they form barriers to transport. Such tori foliate the phase space of integrable, volume-preserving maps with one action and $d$ angles. For the area-preserving case, Greene's residue criterion is often used to predict the destruction of tori from the properties of nearby periodic orbits. Even though KAM theory applies to the three-dimensional case, the robustness of tori in such systems is still poorly understood. We study a three-dimensional, reversible, volume-preserving analogue of Chirikov's standard map with one action and two angles. We investigate the preservation and destruction of tori under perturbation by computing the "residue" of nearby periodic orbits. We find tori with Diophantine rotation vectors in the "spiral mean" cubic algebraic field. The residue is used to generate the critical function of the map and find a candidate for the most robust torus.Comment: laTeX, 40 pages, 26 figure

The Near-Infrared Spectrograph (NIRSpec) on the James Webb Space Telescope: I. Overview of the instrument and its capabilities

We provide an overview of the design and capabilities of the near-infrared spectrograph (NIRSpec) onboard the James Webb Space Telescope. NIRSpec is designed to be capable of carrying out low-resolution ($R\!=30\!-330$) prism spectroscopy over the wavelength range $0.6-5.3\!~\mu$m and higher resolution ($R\!=500\!-1340$ or $R\!=1320\!-3600$) grating spectroscopy over $0.7-5.2\!~\mu$m, both in single-object mode employing any one of five fixed slits, or a 3.1$\times$3.2 arcsec$^2$ integral field unit, or in multiobject mode employing a novel programmable micro-shutter device covering a 3.6$\times$3.4~arcmin$^2$ field of view. The all-reflective optical chain of NIRSpec and the performance of its different components are described, and some of the trade-offs made in designing the instrument are touched upon. The faint-end spectrophotometric sensitivity expected of NIRSpec, as well as its dependency on the energetic particle environment that its two detector arrays are likely to be subjected to in orbit are also discussed

The Near-Infrared Spectrograph (NIRSpec) on the James Webb Space Telescope: I. Overview of the instrument and its capabilities

We provide an overview of the design and capabilities of the near-infrared spectrograph (NIRSpec) onboard the James Webb Space Telescope. NIRSpec is designed to be capable of carrying out low-resolution ($R\!=30\!-330$) prism spectroscopy over the wavelength range $0.6-5.3\!~\mu$m and higher resolution ($R\!=500\!-1340$ or $R\!=1320\!-3600$) grating spectroscopy over $0.7-5.2\!~\mu$m, both in single-object mode employing any one of five fixed slits, or a 3.1$\times$3.2 arcsec$^2$ integral field unit, or in multiobject mode employing a novel programmable micro-shutter device covering a 3.6$\times$3.4~arcmin$^2$ field of view. The all-reflective optical chain of NIRSpec and the performance of its different components are described, and some of the trade-offs made in designing the instrument are touched upon. The faint-end spectrophotometric sensitivity expected of NIRSpec, as well as its dependency on the energetic particle environment that its two detector arrays are likely to be subjected to in orbit are also discussed

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least $4m$. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the $6.5m$ James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 years, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space Telescope Overview, 29 pages, 4 figure

How gold is the golden ratio?

We discuss the well-known importance of the golden ratio in Science and Art with few examples: its theoretical value is often taken as a good model in many applications. How good is this model in practice? We agree with many authors that more precision is needed giving, when possible, a measure of the best possible approximation. We deal with several definitions and representations, also comparing this irrational number and its rational approximations to other similar constants