5,932 research outputs found
The Gauss map on a class of interval translation mappings
We study the dynamics of a class of interval translation map on three
intervals. We show that in this class the typical ITM is of finite type (reduce
to an interval exchange transformation) and that the complement contains a
Cantor set. We relate our maps to substitution subshifts. Results on Hausdorff
dimension of the attractor and on unique ergodicity are obtained
On `observable' Li-Yorke tuples for interval maps
In this paper we study the set of Li-Yorke -tuples and its -dimensional
Lebesgue measure for interval maps . If a
topologically mixing preserves an absolutely continuous probability measure
9with respect to Lebesgue), then the -tuples have Lebesgue full measure, but
if preserves an infinite absolutely continuous measure, the situation
becomes more interesting. Taking the family of Manneville-Pomeau maps as
example, we show that for any , it is possible that the set of
Li-Yorke -tuples has full Lebesgue measure, but the set of Li-Yorke
-tuples has zero Lebesgue measure
Natural equilibrium states for multimodal maps
This paper is devoted to the study of the thermodynamic formalism for a class
of real multimodal maps. This class contains, but it is larger than,
Collet-Eckmann. For a map in this class, we prove existence and uniqueness of
equilibrium states for the geometric potentials , for the largest
possible interval of parameters . We also study the regularity and convexity
properties of the pressure function, completely characterising the first order
phase transitions. Results concerning the existence of absolutely continuous
invariant measures with respect to the Lebesgue measure are also obtained
On the Lebesgue measure of Li-Yorke pairs for interval maps
We investigate the prevalence of Li-Yorke pairs for and
multimodal maps with non-flat critical points. We show that every
measurable scrambled set has zero Lebesgue measure and that all strongly
wandering sets have zero Lebesgue measure, as does the set of pairs of
asymptotic (but not asymptotically periodic) points.
If is topologically mixing and has no Cantor attractor, then typical
(w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally
admits an absolutely continuous invariant probability measure (acip), then
typical pairs have a dense orbit for . These results make use of
so-called nice neighborhoods of the critical set of general multimodal maps,
and hence uniformly expanding Markov induced maps, the existence of either is
proved in this paper as well.
For the setting where has a Cantor attractor, we present a trichotomy
explaining when the set of Li-Yorke pairs and distal pairs have positive
two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure
Equilibrium states for potentials with \sup\phi - \inf\phi < \htop(f)
In the context of smooth interval maps, we study an inducing scheme approach
to prove existence and uniqueness of equilibrium states for potentials
with he `bounded range' condition \sup \phi - \inf \phi < \htop, first used
by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of
Perron-Frobenius operators. We demonstrate that this `bounded range' condition
on the potential is important even if the potential is H\"older continuous. We
also prove analyticity of the pressure in this context.Comment: Added Lemma 6 to deal with the disparity between leading eigenvalues
and operator norms. Added extra references and corrected some typo
Complex maps without invariant densities
We consider complex polynomials for and
, and find some combinatorial types and values of such that
there is no invariant probability measure equivalent to conformal measure on
the Julia set. This holds for particular Fibonacci-like and Feigenbaum
combinatorial types when sufficiently large and also for a class of
`long-branched' maps of any critical order.Comment: Typos corrected, minor changes, principally to Section
Costs and benefits of adapting to climate change at six meters below sea level
Climate change increases the vulnerability of low-lying coastal areas. Careful spatial planning can reduce this vulnerability. An assessment framework aimed at reducing vulnerability to climate change enables decision-makers to make better informed decisions about investments in adaptation to climate change through spatial planning. This paper presents and evaluates an approach to assess adaptation options, with the use of cost-benefit analysis
Top-Down Composition of Software Architectures
This paper discusses an approach for top-down composition of software architectures. First, an architecture is derived that addresses functional requirements only. This architecture contains a number of variability points which are next filled in to address quality concerns. The quality requirements and associated architectural solution fragments are captured in a so-called Feature-Solution (FS) graph. The solution fragments captured in this graph are used to iteratively compose an architecture. Our versatile composition technique allows for pre- and post-refinements, and refinements that involve multiple variability points. In addition, the usage of the FS graph supports Aspect-Oriented Programming (AOP) at the architecture level
The Dolgopyat inequality in bounded variation for non-Markov maps
This is the author accepted manuscript. The final version is available from World Scientific via the DOI in this record.Let F be a (non-Markov) countably piecewise expanding interval map satisfying certain regularity conditions, and Ł˜Ł̃ the corresponding transfer operator. We prove the Dolgopyat inequality for the twisted operator Ł˜s(v)=Ł˜s(esφv)Ł̃s(v)=Ł̃s(esφv) acting on the space BV of functions of bounded variation, where φφ is a piecewise C1C1 roof function.We are also grateful for the support the Erwin
Schrodinger Institute in Vienna, where this paper was completed
- …