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262,176
HEAVINESS IN CIRCLE ROTATIONS
, 906
"... Abstract. We are concerned with describing the structure of the set of points in the unit interval which, when subjected to rotation by irrational α modulo one, for all finite portions of the orbit contain at least as many points in the bottom half of the interval as in the top half. Specifically, a ..."
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Abstract. We are concerned with describing the structure of the set of points in the unit interval which, when subjected to rotation by irrational α modulo one, for all finite portions of the orbit contain at least as many points in the bottom half of the interval as in the top half. Specifically
ON CIRCLE ROTATIONS AND THE SHRINKING TARGET PROPERTIES
, 2007
"... Abstract. We give a necessary and sufficient condition for a circle rotation to have the sexponent monotone shrinking target property (sMSTP), and, thereby, we generalize a result for s = 1 that was established by J. Kurzweil and rediscovered by B. Fayad. As another application of our technique, we ..."
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Cited by 14 (4 self)
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Abstract. We give a necessary and sufficient condition for a circle rotation to have the sexponent monotone shrinking target property (sMSTP), and, thereby, we generalize a result for s = 1 that was established by J. Kurzweil and rediscovered by B. Fayad. As another application of our technique
COHOMOLOGY OF LIPSCHITZ AND ABSOLUTELY CONTINUOUS COCYCLES OVER IRRATIONAL CIRCLE ROTATIONS
"... Abstract. Let Tbe the unit circle with an irrational rotation T: x 7! x+ mod 1, F a real or circle valued cocycle (i.e. we consider cylinder
ows and Anzai skew products). A 0 and L 0 are the Banach spaces of zero mean absolutely continuous, respectively Lipschitz (real or Tvalued) cocycles. Two c ..."
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Abstract. Let Tbe the unit circle with an irrational rotation T: x 7! x+ mod 1, F a real or circle valued cocycle (i.e. we consider cylinder
ows and Anzai skew products). A 0 and L 0 are the Banach spaces of zero mean absolutely continuous, respectively Lipschitz (real or Tvalued) cocycles. Two
Comment.Math.Univ.Carolin. 36,4 (1995)745–764 745 Constructions of smooth and analytic
"... cocycles over irrational circle rotations ..."
Rotating an interval and a circle
 Trans. Amer. Math. Soc
, 1999
"... Abstract. We compare periodic orbits of circle rotations with their counterparts for interval maps. We prove that they are conjugate via a map of modality larger by at most 2 than the modality of the interval map. The proof is based on observation of trips of inhabitants of the Green Islands in the ..."
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Cited by 1 (0 self)
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Abstract. We compare periodic orbits of circle rotations with their counterparts for interval maps. We prove that they are conjugate via a map of modality larger by at most 2 than the modality of the interval map. The proof is based on observation of trips of inhabitants of the Green Islands
RHex: A simple and highly mobile hexapod robot
, 2001
"... In this paper, the authors describe the design and control of RHex, a power autonomous, untethered, compliantlegged hexapod robot. RHex has only six actuators—one motor located at each hip— achieving mechanical simplicity that promotes reliable and robust operation in realworld tasks. Empirically ..."
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Cited by 312 (53 self)
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stable and highly maneuverable locomotion arises from a very simple clockdriven, openloop tripod gait. The legs rotate full circle, thereby preventing the common problem of toe stubbing in the protraction (swing) phase. An extensive suite of experimental results documents the robot’s sig
ROTATION NUMBERS FOR RANDOM DYNAMICAL SYSTEMS ON THE CIRCLE
, 2006
"... Abstract. In this paper, we study rotation numbers of random dynamical systems on the circle. We prove the existence of rotation numbers and the continuous dependence of rotation numbers on the systems. As an application, we prove a theorem on analytic conjugacy to a circle rotation. 1. ..."
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Cited by 9 (0 self)
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Abstract. In this paper, we study rotation numbers of random dynamical systems on the circle. We prove the existence of rotation numbers and the continuous dependence of rotation numbers on the systems. As an application, we prove a theorem on analytic conjugacy to a circle rotation. 1.
Rendering with concentric mosaics
 in Proc. SIGGRAPH
, 1999
"... This paper presents a novel 3D plenoptic function, which we call concentric mosaics. We constrain camera motion to planar concentric circles, and create concentric mosaics using a manifold mosaic for each circle (i.e., composing slit images taken at different locations). Concentric mosaics index all ..."
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Cited by 243 (29 self)
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This paper presents a novel 3D plenoptic function, which we call concentric mosaics. We constrain camera motion to planar concentric circles, and create concentric mosaics using a manifold mosaic for each circle (i.e., composing slit images taken at different locations). Concentric mosaics index
Rotation sets for networks of circle maps
, 2005
"... We consider continuous maps of the torus, homotopic to the identity, that arise from systems of coupled circle maps and discuss the relationship between network architecture and rotation sets. Our main result is that when the map on the torus is invertible, network architecture can force the set of ..."
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We consider continuous maps of the torus, homotopic to the identity, that arise from systems of coupled circle maps and discuss the relationship between network architecture and rotation sets. Our main result is that when the map on the torus is invertible, network architecture can force the set
Results 1  10
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262,176