scholarly journals Connected escaping sets of exponential maps

2011 ◽  
Vol 36 ◽  
pp. 71-80 ◽  
Author(s):  
Lasse Rempe
Keyword(s):  
Exponential Maps

scholarly journals On the dimension of points which escape to infinity at given rate under exponential iteration

2021 ◽  
pp. 1-33
Author(s):  
KRZYSZTOF BARAŃSKI ◽  
BOGUSŁAWA KARPIŃSKA
Keyword(s):  
Packing Dimension ◽  
Exponential Maps

Abstract We prove a number of results concerning the Hausdorff and packing dimension of sets of points which escape (at least in average) to infinity at a given rate under non-autonomous iteration of exponential maps. In particular, we generalize the results proved by Sixsmith in 2016 and answer his question on annular itineraries for exponential maps.

scholarly journals FIXED POINTS OF A FAMILY OF EXPONENTIAL MAPS

2005 ◽  
Vol 24 (3) ◽  
Author(s):  
ERIC BLABAC ◽  
JUSTIN PETERS
Keyword(s):  
Fixed Points ◽  
Exponential Maps

scholarly journals Interactive decal compositing with discrete exponential maps

2006 ◽  
Vol 25 (3) ◽  
pp. 605-613 ◽  
Author(s):  
Ryan Schmidt ◽  
Cindy Grimm ◽  
Brian Wyvill
Keyword(s):  
Exponential Maps

On the Group of Almost Periodic Diffeomorphisms and its Exponential Map

2019 ◽  
Author(s):  
Xu Sun ◽  
Peter Topalov
Keyword(s):  
Lie Group ◽  
Riemannian Metric ◽  
Conjugate Points ◽  
Exponential Map ◽  
Almost Periodic ◽  
Exponential Maps ◽  
Fluid Equations ◽  
Periodic Diffeomorphisms

Abstract We define the group of almost periodic diffeomorphisms on $\mathbb{R}^n$ and on an arbitrary Lie group. We then study the properties of its Riemannian and Lie group exponential maps and provide applications to fluid equations. In particular, we show that there exists a geodesic of a weak Riemannian metric on the group of almost periodic diffeomorphisms of the line that consists entirely of conjugate points.

Parameter rays in the space of exponential maps

2009 ◽  
Vol 29 (2) ◽  
pp. 515-544 ◽  
Author(s):  
MARKUS FÖRSTER ◽  
DIERK SCHLEICHER
Keyword(s):  
Parameter Space ◽  
Complete Classification ◽  
Detailed Structure ◽  
Exponential Parameter ◽  
Singular Orbit ◽  
Exponential Maps

AbstractWe investigate the setIof parametersκ∈ℂ for which the singular orbit (0,eκ,…) ofEκ(z):=exp (z+κ) converges to$\infty $. These parameters are organized in curves in parameter space calledparameter rays, together with endpoints of certain rays. Parameter rays are an important tool to understand the detailed structure of exponential parameter space. In this paper, we construct and investigate these parameter rays. Based on these results, a complete classification of the setIis given in the following paper [M. Förster, L. Rempe and D. Schleicher. Classification of escaping exponential maps.Proc. Amer. Math. Soc.136(2008), 651–663].

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