Normal forms á la moser for aperiodically time-dependent hamiltonians in the vicinity of a hyperbolic equilibrium

The classical theorem of Moser, on the existence of a normal form in the neighbourhood of a hyperbolic equilibrium, is extended to a class of real-analytic Hamiltonians with aperiodically time-dependent perturbations. A stronger result is obtained in the case in which the perturbing function exhibits a time decay

Late-Summer Abundance and Distribution of Marine Birds in Kasegaluk Lagoon, Chukchi Sea, Alaska

Oil and gas drilling programs in the Alaska Chukchi Sea were carried out on leases offshore from Kasegaluk Lagoon in 1989-91, and further exploration and development activities in this area are likely in future years. We conducted aerial surveys between late July and early September 1989-91 to determine the distribution and abundance of marine birds in the Kasegaluk Lagoon area. We hypothesized that Kasegaluk Lagoon supported an avifauna similar to that found in other lagoon systems in arctic Alaska. In fact, the richness and diversity of bird species using Kasegaluk Lagoon were greater than in lagoon systems in the Beaufort Sea. Brant (Branta bernicla) was the most abundant species in Kasegaluk Lagoon compared to lagoons in the Beaufort Sea, where the Oldsquaw (Clangula hyemalis) is the dominant species. Several other species or species groups, such as Glaucous Gull (Larus hyperboreus), Arctic Tern (Sterna Paradisaea), small shorebirds (mainly Calidris and Phalaropus), and Lesser Snow Goose (Chen caerulescens) were also relatively abundant in Kasegaluk Lagoon.Key words: waterbirds, aerial surveys, lagoon ecosystems, Kasegaluk Lagoon, Chukchi Sea, Beaufort Sea, AlaskaDes programmes de forage pétrolier et gazier ont été exécutés dans la portion alaskienne de la mer des Tchouktches, sur des concessions au large de l'étang côtier Kasegaluk de 1989 à 1991, et on prévoit que d'autres activités reliées à l'exploration et au développement auront lieu à cet endroit dans les années à venir. On a effectué des relevés aériens entre la fin de juillet et le début de septembre de 1989 à 1991, afin de déterminer la distribution et l'abondance des oiseaux marins dans la région de l'étang côtier Kasegaluk. On avait émis l'hypothèse que cet étang était le refuge d'une avifaune semblable à celle qui se trouve dans d'autres systèmes lagunaires dans l'Alaska arctique. En réalité, la richesse et la diversité des espèces d'oiseaux utilisant l'étang Kasegaluk étaient supérieures à celles des systèmes lagunaires de la mer de Beaufort. La bernache cravant (Branta bernicla) représentait l'espèce la plus abondante de l'étang côtier Kasegaluk comparé aux étangs côtiers de la mer de Beaufort, où le canard kakawi (Clangula hyemalis) est l'espèce dominante. Plusieurs autres espèces ou groupes d'espèces, comme le goéland bourgmestre (Larus hyperboreus), la sterne arctique (Sterna paradisaea), les petits oiseaux de rivage (surtout Calidris et Phalaropus) et la petite oie blanche (Chen caerulescens) étaient relativement abondants dans l'étang côtier Kasegaluk.Mots clés : oiseaux aquatiques, relevés aériense,écosystèmes lagunaires, étang côtier Kasegaluk, mer des Tchouktches, mer de Beaufort, Alask

The Chaotic Saddle in the Lozi Map, Autonomous and Nonautonomous Versions

In this paper, we prove the existence of a chaotic saddle for a piecewise-linear map of the plane, referred to as the Lozi map. We study the Lozi map in its orientation and area preserving version. First, we consider the autonomous version of the Lozi map to which we apply the Conley–Moser conditions to obtain the proof of a chaotic saddle. Then we generalize the Lozi map on a nonautonomous version and we prove that the first and the third Conley–Moser conditions are satisfied, which imply the existence of a chaotic saddle. Finally, we numerically demonstrate how the structure of this nonautonomous chaotic saddle varies as parameters are varied. </jats:p

Chaotic Dynamics in Nonautonomous Maps:Application to the Nonautonomous Hénon Map

In this paper, we analyze chaotic dynamics for two-dimensional nonautonomous maps through the use of a nonautonomous version of the Conley–Moser conditions given previously. With this approach we are able to give a precise definition of what is meant by a chaotic invariant set for nonautonomous maps. We extend the nonautonomous Conley–Moser conditions by deriving a new sufficient condition for the nonautonomous chaotic invariant set to be hyperbolic. We consider the specific example of a nonautonomous Hénon map and give sufficient conditions, in terms of the parameters defining the map, for the nonautonomous Hénon map to have a hyperbolic chaotic invariant set. </jats:p

The efficient computation of transition state resonances and reaction rates from a quantum normal form

A quantum version of a recent formulation of transition state theory in {\em phase space} is presented. The theory developed provides an algorithm to compute quantum reaction rates and the associated Gamov-Siegert resonances with very high accuracy. The algorithm is especially efficient for multi-degree-of-freedom systems where other approaches are no longer feasible.Comment: 4 pages, 3 figures, revtex

Performance of chaos diagnostics based on Lagrangian descriptors. Application to the 4D standard map

We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD) computations of initially nearby orbits to detect chaos in conservative dynamical systems with phase space dimensionality higher than two. In particular, we consider the recently introduced methods of the difference ($D_L^n$) and the ratio ($R_L^n$) of the LDs of neighboring orbits, as well as a quantity ($S_L^n$) related to the finite-difference second spatial derivative of the LDs, and use them to determine the chaotic or regular nature of ensembles of orbits of a prototypical area-preserving map model, the 4-dimensional (4D) symplectic standard map. Using the distributions of the indices' values we determine appropriate thresholds to discriminate between regular and chaotic orbits, and compare the obtained characterization against that achieved by the Smaller Alignment Index (SALI) method of chaos detection, by recording the percentage agreement $P_A$ between the two classifications. We study the influence of various factors on the performance of these indices, and show that the increase of the final number of orbit iterations T and the order n of the indices (i.e. the dimensionality of the space where the considered nearby orbits lie), as well as the decrease of the distance $\sigma$ of neighboring orbits, increase the $P_A$ values along with the required computational effort. Balancing between these two factors we find appropriate T, n and $\sigma$ values, which allow the efficient use of the $D_L^n$, $R_L^n$ and $S_L^n$ indices as short time and computationally cheap chaos diagnostics achieving $P_A \gtrsim 90 \%$, with $D_L^n$ and $S_L^n$ having larger $P_A$ values than $R_L^n$. Our results show that the three LDs-based indices perform better for systems with large percentages of chaotic orbits

Isomerization dynamics of a buckled nanobeam

We analyze the dynamics of a model of a nanobeam under compression. The model is a two mode truncation of the Euler-Bernoulli beam equation subject to compressive stress. We consider parameter regimes where the first mode is unstable and the second mode can be either stable or unstable, and the remaining modes (neglected) are always stable. Material parameters used correspond to silicon. The two mode model Hamiltonian is the sum of a (diagonal) kinetic energy term and a potential energy term. The form of the potential energy function suggests an analogy with isomerisation reactions in chemistry. We therefore study the dynamics of the buckled beam using the conceptual framework established for the theory of isomerisation reactions. When the second mode is stable the potential energy surface has an index one saddle and when the second mode is unstable the potential energy surface has an index two saddle and two index one saddles. Symmetry of the system allows us to construct a phase space dividing surface between the two "isomers" (buckled states). The energy range is sufficiently wide that we can treat the effects of the index one and index two saddles in a unified fashion. We have computed reactive fluxes, mean gap times and reactant phase space volumes for three stress values at several different energies. In all cases the phase space volume swept out by isomerizing trajectories is considerably less than the reactant density of states, proving that the dynamics is highly nonergodic. The associated gap time distributions consist of one or more `pulses' of trajectories. Computation of the reactive flux correlation function shows no sign of a plateau region; rather, the flux exhibits oscillatory decay, indicating that, for the 2-mode model in the physical regime considered, a rate constant for isomerization does not exist.Comment: 42 pages, 6 figure

Phase Space Structures Explain Hydrogen Atom Roaming in Formaldehyde Decomposition

We re-examine the prototypical roaming reaction—hydrogen atom roaming in formaldehyde decomposition—from a phase space perspective. Specifically, we address the question “why do trajectories roam, rather than dissociate through the radical channel?” We describe and compute the phase space structures that define and control all possible reactive events for this reaction, as well as provide a dynamically exact description of the roaming region in phase space. Using these phase space constructs, we show that in the roaming region, there is an unstable periodic orbit whose stable and unstable manifolds define a conduit that both encompasses all roaming trajectories exiting the formaldehyde well and shepherds them toward the H2···CO well

A λ-lemma for Normally Hyperbolic Invariant Manifolds

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