On properties of the vertical rotation interval for twist mappings II

2004 ◽  
Vol 4 (2) ◽  
pp. 125-137
Author(s):  
Salvador Addas-Zanata
Keyword(s):  
Rotation Interval ◽  
Twist Mappings

scholarly journals Stability for the vertical rotation interval of twist mappings

2006 ◽  
Vol 14 (4) ◽  
pp. 631-642
Author(s):  
Salvador Addas-Zanata ◽  
Keyword(s):  
Rotation Interval ◽  
Twist Mappings

The optimal rotation of a flammable forest stand

1980 ◽  
Vol 10 (1) ◽  
pp. 30-34 ◽  
Author(s):  
D. L. Martell
Keyword(s):  
Stochastic Model ◽  
Fire Management ◽  
Jack Pine ◽  
Forest Stand ◽  
Timber Production ◽  
Forest Stands ◽  
Rotation Interval ◽  
Optimal Rotation

The author describes a stochastic model of forest stand rotation which can be used to determine the optimal planned rotation interval for flammable forest stands. The model can also be used to estimate the value of fire management activities in terms of the potential enhanced value of timber production. The use of the model is illustrated by applying it to a simplified case of jack pine (Pinusbanksiana, Lamb.) management.

scholarly journals Prescribed-burning vs. wildfire: management implications for annual carbon emissions along a latitudinal gradient of <i>Calluna vulgaris</i>-dominated vegetation

2015 ◽  
Vol 12 (21) ◽  
pp. 17817-17849
Author(s):  
V. M. Santana ◽  
J. G. Alday ◽  
H. Lee ◽  
K. A. Allen ◽  
R. H. Marrs
Keyword(s):  
Carbon Emissions ◽  
Fire Ecology ◽  
Latitudinal Gradient ◽  
Prescribed Burning ◽  
Biomass Accumulation ◽  
Calluna Vulgaris ◽  
Site Specific ◽  
Litter Accumulation ◽  
Rotation Interval ◽  
Annual Carbon

Abstract. A~present challenge in fire ecology is to optimize management techniques so that ecological services are maximized and C emissions minimized. Here, we model the effects of different prescribed-burning rotation intervals and wildfires on carbon emissions (present and future) in British moorlands. Biomass-accumulation curves from four Calluna-dominated ecosystems along a north–south, climatic gradient in Great Britain were calculated and used within a matrix-model based on Markov Chains to calculate above-ground biomass-loads, and annual C losses under different prescribed-burning rotation intervals. Additionally, we assessed the interaction of these parameters with an increasing wildfire return interval. We observed that litter accumulation patterns varied along the latitudinal gradient, with differences between northern (colder and wetter) and southern sites (hotter and drier). The accumulation patterns of the living vegetation dominated by Calluna were determined by site-specific conditions. The optimal prescribed-burning rotation interval for minimizing annual carbon losses also differed between sites: the rotation interval for northern sites was between 30 and 50 years, whereas for southern sites a hump-backed relationship was found with the optimal interval either between 8 to 10 years or between 30 to 50 years. Increasing wildfire frequency interacted with prescribed-burning rotation intervals by both increasing C emissions and modifying the optimum prescribed-burning interval for C minimum emission. This highlights the importance of studying site-specific biomass accumulation patterns with respect to environmental conditions for identifying suitable fire-rotation intervals to minimize C losses.

scholarly journals ROTATION SETS FOR ORBITS OF DEGREE ONE CIRCLE MAPS

2002 ◽  
Vol 12 (02) ◽  
pp. 429-437
Author(s):  
LLUÍS ALSEDÀ ◽  
FRANCESC MAÑOSAS ◽  
MOIRA CHAS
Keyword(s):  
Circle Map ◽  
Circle Maps ◽  
Rotation Interval ◽  
The One ◽  
Rotation Set ◽  
Dynamical Information

Let F be the lifting of a circle map of degree one. In [Bamón et al., 1984] a notion of F-rotation interval of a point [Formula: see text] was given. In this paper we define and study a new notion of a rotation set of point which preserves more of the dynamical information contained in the sequences [Formula: see text] than the one preserved from [Bamón et al., 1984]. In particular, we characterize dynamically the endpoints of these sets and we obtain an analogous version of the Main Theorem of [Bamón et al., 1984] in our settings.

scholarly journals Twist sets for maps of the circle

1984 ◽  
Vol 4 (3) ◽  
pp. 391-404 ◽  
Author(s):  
Michał Misiurewicz
Keyword(s):  
Rotation Number ◽  
Closed Set ◽  
Twist Map ◽  
Rotation Interval ◽  
Continuous Map ◽  
The One

AbstractLet f be a continuous map of degree one of the circle onto itself. We prove that for every number a from the rotation interval of f there exists an invariant closed set A consisting of points with rotation number a and such that f restricted to A preserves the order. This result is analogous to the one in the case of a twist map of an annulus.

OBSERVED ROTATION NUMBERS IN FAMILIES OF CIRCLE MAPS

2001 ◽  
Vol 11 (01) ◽  
pp. 73-89 ◽  
Author(s):  
MICHAEL A. SAUM ◽  
TODD R. YOUNG
Keyword(s):  
Lebesgue Measure ◽  
Rotation Number ◽  
Narrow Band ◽  
Initial Conditions ◽  
Positive Probability ◽  
Circle Maps ◽  
Numerical Evidence ◽  
Rotation Interval ◽  
Large Numbers ◽  
Rotation Numbers

Noninvertible circle maps may have a rotation interval instead of a unique rotation number. One may ask which of the numbers or sets of numbers within this rotation interval may be observed with positive probability in term of Lebesgue measure on the circle. We study this question numerically for families of circle maps. Both the interval and "observed" rotation numbers are computed for large numbers of initial conditions. The numerical evidence suggests that within the rotation interval only a very narrow band or even a unique rotation number is observed. These observed rotation numbers appear to be either locally constant or vary wildly as the parameter is changed. Closer examination reveals that intervals with wild variation contain many subintervals where the observed rotation numbers are locally constant. We discuss the formation of these intervals. We prove that such intervals occur whenever one of the endpoints of the rotation interval changes. We also examine the effects of various types of saddle-node bifurcations on the observed rotation numbers.

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