• 제목/요약/키워드: conjugacy invariant

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INVARIANCE OF KNEADING MATRIX UNDER CONJUGACY

  • Gopalakrishna, Chaitanya;Veerapazham, Murugan
    • 대한수학회지
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    • 제58권2호
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    • pp.265-281
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    • 2021
  • In the kneading theory developed by Milnor and Thurston, it is proved that the kneading matrix and the kneading determinant associated with a continuous piecewise monotone map are invariant under orientation-preserving conjugacy. This paper considers the problem for orientation-reversing conjugacy and proves that the former is not an invariant while the latter is. It also presents applications of the result towards the computational complexity of kneading matrices and the classification of maps up to topological conjugacy.

A CYCLIC GROUP ACTION ON THE NILMANIFOLD

  • Shin, Joonkook;Kim, Jong-Il
    • 충청수학회지
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    • 제13권2호
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    • pp.71-79
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    • 2001
  • We study only free actions of finite abelian groups G on the 3-dimensional nilmanifold, up to topological conjugacy. we shall deal with only one out of 15 distinct almost Bieberbach groups up to Seifert local invariant.

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FREE CYCLIC ACTIONS OF THE 3-DIMENSIONAL NILMANIFOLD

  • Shin, Joonkook;Goo, Daehwan;Park, Eunmi
    • 충청수학회지
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    • 제14권2호
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    • pp.27-35
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    • 2001
  • We shall deal with ten cases out of 15 distinct almost Bieberbach groups up to Seifert local invariant. In those cases we will show that if G is a finite abelian group acting freely on the standard nilmanifold, then G is cyclic, up to topological conjugacy.

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VARIOUS SHADOWING PROPERTIES FOR TIME VARYING MAPS

  • Sarkooh, Javad Nazarian
    • 대한수학회보
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    • 제59권2호
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    • pp.481-506
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    • 2022
  • This paper is concerned with the study of various notions of shadowing of dynamical systems induced by a sequence of maps, so-called time varying maps, on a metric space. We define and study the shadowing, h-shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties of these dynamical systems. We show that h-shadowing, limit shadowing and s-limit shadowing properties are conjugacy invariant. Also, we investigate the relationships between these notions of shadowing for time varying maps and examine the role that expansivity plays in shadowing properties of such dynamical systems. Specially, we prove some results linking s-limit shadowing property to limit shadowing property, and h-shadowing property to s-limit shadowing and limit shadowing properties. Moreover, under the assumption of expansivity, we show that the shadowing property implies the h-shadowing, s-limit shadowing and limit shadowing properties. Finally, it is proved that the uniformly contracting and uniformly expanding time varying maps exhibit the shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties.