scholarly journals Invariant Varieties of Periodic Points for Some Higher Dimensional Integrable Maps

2007 ◽  
Vol 76 (2) ◽  
pp. 024006 ◽  
Author(s):  
Satoru Saito ◽  
Noriko Saitoh
Keyword(s):  
Periodic Points ◽  
Higher Dimensional ◽  
Invariant Varieties

scholarly journals Periodic points of solenoidal automorphisms in terms of inverse limits

2021 ◽  
Vol 22 (2) ◽  
pp. 321
Author(s):  
Sharan Gopal ◽  
Faiz Imam
Keyword(s):  
Inverse Limit ◽  
Periodic Points ◽  
Inverse Limits ◽  
One Dimensional ◽  
Higher Dimensional

<p>In this paper, we describe the periodic points of automorphisms of a one dimensional solenoid, considering it as the inverse limit, lim←k (S 1 , γk) of a sequence (γk) of maps on the circle S 1 . The periodic points are discussed for a class of automorphisms on some higher dimensional solenoids also.</p>

scholarly journals Automorphisms of compact groups

1989 ◽  
Vol 9 (4) ◽  
pp. 691-735 ◽  
Author(s):  
Bruce Kitchens ◽  
Klaus Schmidt
Keyword(s):  
Lie Group ◽  
Invariant Subgroup ◽  
Chain Condition ◽  
Periodic Points ◽  
Compact Lie Group ◽  
Higher Dimensional ◽  
Metrizable Group ◽  
Algebraic Description ◽  
Descending Chain Condition ◽  
Dense Set

AbstractWe study finitely generated, abelian groups Γ of continuous automorphisms of a compact, metrizable group X and introduce the descending chain condition for such pairs (X, Γ). If Γ acts expansively on X then (X, Γ) satisfies the descending chain condition, and (X, Γ) satisfies the descending chain condition if and only if it is algebraically and topologically isomorphic to a closed, shift-invariant subgroup of GΓ, where G is a compact Lie group. Furthermore every such subgroup of GΓ is a (higher dimensional) Markov shift whose alphabet is a compact Lie group. By using the descending chain condition we prove, for example, that the set of Γ-periodic points is dense in X whenever Γ acts expansively on X. Furthermore, if X is a compact group and (X, Γ) satisfies the descending chain condition, then every ergodic element of Γ has a dense set of periodic points. Finally we give an algebraic description of pairs (X, Γ) satisfying the descending chain condition under the assumption that X is abelian.

Weak Gibbs measures for certain non-hyperbolic systems

2000 ◽  
Vol 20 (5) ◽  
pp. 1495-1518 ◽  
Author(s):  
MICHIKO YURI
Keyword(s):  
Bounded Variation ◽  
Invariant Measures ◽  
Hyperbolic Systems ◽  
Gibbs Measures ◽  
Periodic Points ◽  
Statistical Properties ◽  
Equilibrium States ◽  
Pointwise Dimension ◽  
Absolutely Continuous ◽  
Higher Dimensional

We study a weak Gibbs property of equilibrium states for potentials of weak bounded variation and for maps admitting indifferent periodic points. We further establish statistical properties of the weak Gibbs measures and bounds of their pointwise dimension. We apply our results to higher-dimensional maps (which are not necessarily conformal) with indifferent periodic points and show that their absolutely continuous finite invariant measures are weak Gibbs measures.

Spectroscopy-Based Mapping with Scanning Microwave Impedance Microscopy

2018 ◽  
Author(s):  
Peter De Wolf ◽  
Zhuangqun Huang ◽  
Bede Pittenger
Keyword(s):  
Single Point ◽  
Electrical Characterization ◽  
Principal Component ◽  
High Sensitivity ◽  
Data Cube ◽  
Nanometer Scale ◽  
Learning Approaches ◽  
Data Set ◽  
3D Data ◽  
Higher Dimensional

Abstract Methods are available to measure conductivity, charge, surface potential, carrier density, piezo-electric and other electrical properties with nanometer scale resolution. One of these methods, scanning microwave impedance microscopy (sMIM), has gained interest due to its capability to measure the full impedance (capacitance and resistive part) with high sensitivity and high spatial resolution. This paper introduces a novel data-cube approach that combines sMIM imaging and sMIM point spectroscopy, producing an integrated and complete 3D data set. This approach replaces the subjective approach of guessing locations of interest (for single point spectroscopy) with a big data approach resulting in higher dimensional data that can be sliced along any axis or plane and is conducive to principal component analysis or other machine learning approaches to data reduction. The data-cube approach is also applicable to other AFM-based electrical characterization modes.

HIGHER DIMENSIONAL ROBERTSON WALKER UNIVERSES INTERACTING WITH BRANS-DICKE FIELD

2020 ◽  
Vol 9 (10) ◽  
pp. 8545-8557
Author(s):  
K. P. Singh ◽  
T. A. Singh ◽  
M. Daimary
Keyword(s):  
Higher Dimensional
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