3,663 research outputs found
Distribution of periodic points of polynomial diffeomorphisms of C^2
This paper deals with the dynamics of a simple family of holomorphic
diffeomorphisms of \C^2: the polynomial automorphisms. This family of maps
has been studied by a number of authors. We refer to [BLS] for a general
introduction to this class of dynamical systems. An interesting object from the
point of view of potential theory is the equilibrium measure of the set
of points with bounded orbits. In [BLS] is also characterized
dynamically as the unique measure of maximal entropy. Thus is also an
equilibrium measure from the point of view of the thermodynamical formalism. In
the present paper we give another dynamical interpretation of as the
limit distribution of the periodic points of
Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents
This paper concerns the dynamics of polynomial automorphisms of .
One can associate to such an automorphism two currents and the
equilibrium measure . In this paper we study some
geometric and dynamical properties of these objects. First, we characterize
as the unique measure of maximal entropy. Then we show that the measure
has a local product structure and that the currents have a
laminar structure. This allows us to deduce information about periodic points
and heteroclinic intersections. For example, we prove that the support of
coincides with the closure of the set of saddle points. The methods used
combine the pluripotential theory with the theory of non-uniformly hyperbolic
dynamical systems
Observations of the biological communities at Bolsa Chica artificial reef
Bolsa Chica Artificial Reef (BCAR) was constructed in
November 1986 with 10,400 tons of concrete rubble and
eight concrete and steel barges. Prior to any additional
augmentation of BCAR, the u.s. Army Corps of Engineers
and the California Coastal Commission required the
California Department of Fish and Game (CDFG) to survey
the bioloqical communities on and around BCAR.
In April 1992, qualitative surveys of the biological
communities were conducted on one of the eight modules at
BCAR and at a nearby sand-only site. One of the modules,
Module D, located in 90 feet of water (MLLW), was
surveyed for fish, macroinvertebrates, and turf community
organisms (small plants and sessile animals). Twelve
species of fish were observed, including kelp bass
(Paralabrax clathratus) and barred sand bass (P.
nebulifer). Eight macroinvertebrate species were
observed, rock scallops (Crassedoma giganteum) being the
most abundant. The turf community was comprised of
thirteen invertebrate taxa, among which erect ectoprocts
(Bugula spp.) were the most numerous. Two species of
foliose red algae (Rhodymenia pacifica and Anisocladella
pacifica) were also observed.
The reef has reached an advanced stage of successional
development with fish and invertebrate communities
diverse and well established. However, due,.to its depth
and the turbidity of surrounding waters, this reef is not
likely to ever support a diverse algal community.
The diversity and abundance of fish and
macroinvertebrates were, as to be expected, much lower in
the nearby sand-only site. Only two species of fish and
seven macroinvertebrate species were observed. Of these,
only the sea pen, Stylatula elongata, was common.
Overall, when compared to nearby sand-only habitats,
Bolsa Chica Artificial Reef appears to contribute
substantially to the local biological productivity. In
addition, the concrete rubble used in BCAR' s construction
appears to be performing as well as the quarry rock used
in all of CDFG's experimental reefs. (Document pdf contains 22 pages
Post-critical set and non existence of preserved meromorphic two-forms
We present a family of birational transformations in depending on
two, or three, parameters which does not, generically, preserve meromorphic
two-forms. With the introduction of the orbit of the critical set (vanishing
condition of the Jacobian), also called ``post-critical set'', we get some new
structures, some "non-analytic" two-form which reduce to meromorphic two-forms
for particular subvarieties in the parameter space. On these subvarieties, the
iterates of the critical set have a polynomial growth in the \emph{degrees of
the parameters}, while one has an exponential growth out of these subspaces.
The analysis of our birational transformation in is first carried out
using Diller-Favre criterion in order to find the complexity reduction of the
mapping. The integrable cases are found. The identification between the
complexity growth and the topological entropy is, one more time, verified. We
perform plots of the post-critical set, as well as calculations of Lyapunov
exponents for many orbits, confirming that generically no meromorphic two-form
can be preserved for this mapping. These birational transformations in ,
which, generically, do not preserve any meromorphic two-form, are extremely
similar to other birational transformations we previously studied, which do
preserve meromorphic two-forms. We note that these two sets of birational
transformations exhibit totally similar results as far as topological
complexity is concerned, but drastically different results as far as a more
``probabilistic'' approach of dynamical systems is concerned (Lyapunov
exponents). With these examples we see that the existence of a preserved
meromorphic two-form explains most of the (numerical) discrepancy between the
topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure
Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs
Physicists have argued that periodic orbit bunching leads to universal
spectral fluctuations for chaotic quantum systems. To establish a more detailed
mathematical understanding of this fact, it is first necessary to look more
closely at the classical side of the problem and determine orbit pairs
consisting of orbits which have similar actions. In this paper we specialize to
the geodesic flow on compact factors of the hyperbolic plane as a classical
chaotic system. We prove the existence of a periodic partner orbit for a given
periodic orbit which has a small-angle self-crossing in configuration space
which is a `2-encounter'; such configurations are called `Sieber-Richter pairs'
in the physics literature. Furthermore, we derive an estimate for the action
difference of the partners. In the second part of this paper [13], an inductive
argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit
What is the value of a standard?
Standards play a critical role in the procurement of defence, and other, systems. Choosing the most appropriate standard is important but has become more topical given the UK Ministry of Defence policy of “as civilian as possible, as military as necessary”. Whereas historically managers might have selected from classes of defence standards, this choice set is now increased to include civil standards. We develop a model that has been commissioned by the UK Defence Standardisation whose responsibilities include supporting project teams on the selection of standards. Our model is based on an extension of Bayesian Belief Networks, called an Influence Diagram, which allows decisions and consequences to be represented as well as uncertain-ties. We have developed an initial model for a real case to assess the feasibility and use. We outline the con-text of the defence procurement project in our case study and describe the reasoning underpinning the model structure. We have found that it is possible to develop a simple model that captures the views of multiple stakeholders and informs a reasoned choice about the value of alternative standards
Non-uniqueness of ergodic measures with full Hausdorff dimension on a Gatzouras-Lalley carpet
In this note, we show that on certain Gatzouras-Lalley carpet, there exist
more than one ergodic measures with full Hausdorff dimension. This gives a
negative answer to a conjecture of Gatzouras and Peres
Discovery of Anion Insertion Electrochemistry in Layered Hydroxide Nanomaterials
Electrode materials which undergo anion insertion are a void in the materials innovation landscape and a missing link to energy efficient electrochemical desalination. In recent years layered hydroxides (LHs) have been studied for a range of electrochemical applications, but to date have not been considered as electrode materials for anion insertion electrochemistry. Here, we show reversible anion insertion in a LH for the first time using Co and Co-V layer hydroxides. By pairing in situ synchrotron and quartz crystal microbalance measurements with a computational unified electrochemical band-diagram description, we reveal a previously undescribed anion-insertion mechanism occurring in Co and Co-V LHs. This proof of concept study demonstrates reversible electrochemical anion insertion in LHs without significant material optimization. These results coupled with our foundational understanding of anion insertion electrochemistry establishes LHs as a materials platform for anion insertion electrochemistry with the potential for future application to electrochemical desalination
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