1,579 research outputs found
Exponential speed of mixing for skew-products with singularities
Let be the
endomorphism given by where is a positive real number. We prove that is
topologically mixing and if then is mixing with respect to Lebesgue
measure. Furthermore we prove that the speed of mixing is exponential.Comment: 23 pages, 3 figure
Robust entropy expansiveness implies generic domination
Let be a -diffeomorphism, , defined on a compact
boundaryless -dimensional manifold , , and let be the
homoclinic class associated to the hyperbolic periodic point . We prove that
if there exists a neighborhood of such that for every
the continuation of is entropy-expansive
then there is a -invariant dominated splitting for of the form
where is contracting, is
expanding and all are one dimensional and not hyperbolic.Comment: 24 page
Recommended from our members
Full effects of land use change in the representative concentration pathways
Future land use change (LUC) is an important component of the IPCC representative concentration pathways (RCPs), but in these scenarios' radiative forcing targets the climate impact of LUC only includes greenhouse gases. However, climate effects due to physical changes of the land surface can be as large. Here we show the critical importance of including non-carbon impacts of LUC when considering the RCPs. Using an ensemble of climate model simulations with and without LUC, we show that the net climate effect is very different from the carbon-only effect. Despite opposite signs of LUC, all the RCPs assessed here have a small net warming from LUC because of varying biogeophysical effects, and in RCP4.5 the warming is outside of the expected variability. The afforestation in RCP4.5 decreases surface albedo, making the net global temperature anomaly over land around five times larger than RCPs 2.6 and 8.5, for around twice the amount of LUC. Consequent changes to circulation in RCP4.5 in turn reduce Arctic sea ice cover. The small net positive temperature effect from LUC could make RCP4.5's universal carbon tax, which incentivizes retaining and growing forest, counter productive with respect to climate. However, there are spatial differences in the balance of impacts, and potential climate gains would need to be assessed against other environmental aims
Large deviations for non-uniformly expanding maps
We obtain large deviation results for non-uniformly expanding maps with
non-flat singularities or criticalities and for partially hyperbolic
non-uniformly expanding attracting sets. That is, given a continuous function
we consider its space average with respect to a physical measure and compare
this with the time averages along orbits of the map, showing that the Lebesgue
measure of the set of points whose time averages stay away from the space
average decays to zero exponentially fast with the number of iterates involved.
As easy by-products we deduce escape rates from subsets of the basins of
physical measures for these types of maps. The rates of decay are naturally
related to the metric entropy and pressure function of the system with respect
to a family of equilibrium states. The corrections added to the published
version of this text appear in bold; see last section for a list of changesComment: 36 pages, 1 figure. After many PhD students and colleagues having
pointed several errors in the statements and proofs, this is a correction to
published article answering those comments. List of main changes in a new
last sectio
- …