Constructing ergodic exponential maps with dense post-singular orbits

2009 ◽  
Vol 30 (1) ◽  
pp. 309-316
Author(s):  
XIUMEI WANG ◽  
GAOFEI ZHANG
Keyword(s):  
Forward Orbit ◽  
Exponential Maps ◽  
Singular Orbits

AbstractWe construct ergodic exponential maps fλ(z)=λez such that the forward orbit of the origin is dense in $\Bbb C$.

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

Investigations on the Rotordynamic Characteristics of a Hole-Pattern Seal Using Transient CFD and Periodic Circular Orbit Model

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Xin Yan ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Circular Orbit ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Numerical Approach ◽  
Deformation Method ◽  
Rotordynamic Coefficients ◽  
Forward Orbit ◽  
Reaction Forces ◽  
Orbit Model

Numerical investigations on the rotordynamic characteristics of a typical hole-pattern seal using transient three-dimensional Reynolds-averaged Navier–Stokes (RANS) solution and the periodic circular orbit model were conducted in this work. The unsteady solutions combined with mesh deformation method were utilized to solve the three-dimensional RANS equations and obtain the transient reaction forces on a typical hole-pattern seal rotor at five different excitation frequencies. The relation between the periodic reaction forces and frequency dependent rotordynamic coefficients of the hole-pattern seal was obtained by considering the rotor with a periodic circular orbit (including forward orbit and backward orbit) of the seal center. The rotordynamic coefficients of the hole-pattern seal were then solved based on the obtained unsteady reaction forces and presented numerical method. Compared with the experimental data, the predicted rotordynamic coefficients of the hole-pattern seal are more agreeable with the experiment than that of the ISO-temperature (ISOT) bulk flow analysis and numerical approach with one-direction-shaking model. Furthermore, the unsteady leakage flow characteristics in the hole-pattern seal were also illustrated and discussed in detail.

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.

scholarly journals SINGULAR ORBITS AND DYNAMICS AT INFINITY OF A CONJUGATE LORENZ-LIKE SYSTEM

2015 ◽  
Vol 20 (2) ◽  
pp. 148-167 ◽  
Author(s):  
Fengjie Geng ◽  
Xianyi Li
Keyword(s):  
Theoretical Analysis ◽  
Lyapunov Exponents ◽  
Heteroclinic Orbits ◽  
Chaotic Attractors ◽  
Heteroclinic Cycles ◽  
Basic Properties ◽  
Homoclinic And Heteroclinic Orbits ◽  
Quadratic Nonlinearities ◽  
Singular Orbits

A conjugate Lorenz-like system which includes only two quadratic nonlinearities is proposed in this paper. Some basic properties of this system, such as the distribution of its equilibria and their stabilities, the Lyapunov exponents, the bifurcations are investigated by some numerical and theoretical analysis. The forming mechanisms of compound structures of its new chaotic attractors obtained by merging together two simple attractors after performing one mirror operation are also presented. Furthermore, some of its other complex dynamical behaviours, which include the existence of singularly degenerate heteroclinic cycles, the existence of homoclinic and heteroclinic orbits and the dynamics at infinity, etc, are formulated in detail. In the meantime, some problems deserving further investigations are presented.

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