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P. Walters (1968)
Topological conjugacy of affine transformations of toriTransactions of the American Mathematical Society, 131
P. Walters (1969)
TOPOLOGICAL CONJUGACY OF AFFINE TRANSFORMATIONS OF COMPACT ABELIAN GROUPSTransactions of the American Mathematical Society, 140
R. Adler, R. Palais (1965)
Homeomorphic conjugacy of automorphisms on the torus, 16
M. Misiurewicz, W. Szlenk (1980)
Entropy of piecewise monotone mappingsStudia Mathematica, 67
J. Buzzi (2007)
Maximal entropy measures for piecewise affine surface homeomorphismsErgodic Theory and Dynamical Systems, 29
Y. Yomdin (1987)
Volume growth and entropyIsrael Journal of Mathematics, 57
S. Sternberg (1957)
Local Contractions and a Theorem of PoincareAmerican Journal of Mathematics, 79
S. Newhouse (1989)
Continuity properties of entropyAnnals of Mathematics, 129
G. Cairns, A. Nielsen (2005)
On the dynamics of the linear action of SL ( n, Z )Bulletin of The Australian Mathematical Society, 71
M. Rees (1981)
A Minimal Positive Entropy Homeomorphism of the 2-TorusJournal of The London Mathematical Society-second Series
S. Dani, Srikanth Raghavan (1980)
Orbits of euclidean frames under discrete linear groupsIsrael Journal of Mathematics, 36
J. Zukas (1998)
Introduction to the Modern Theory of Dynamical SystemsShock and Vibration, 5
B. Hou, Hongzhi Liu, Xiaotian Pan (2017)
Mutual embeddability equivalence relation for rotation algebrasJournal of Mathematical Analysis and Applications, 452
Huaxin Lin (2005)
Furstenberg Transformations and Approximate ConjugacyCanadian Journal of Mathematics, 60
A. Katok (2010)
Nonuniform Hyperbolicity and Structure o Smooth Dynamical Systems
R. Adler, C. Tresser, P. Worfolk (1997)
Topological conjugacy of linear endomorphisms of the 2-torusTransactions of the American Mathematical Society, 349
S. Bhattacharya (2000)
Topological conjugacy of automorphism flows on compact Lie groupsErgodic Theory and Dynamical Systems, 20
Huaxin Lin, H. Matui (2004)
Minimal dynamical systems and approximate conjugacyMathematische Annalen, 332
A Katok (1995)
10.1017/CBO9780511809187
S. Bhattacharya (1999)
Orbit Equivalence and Topological Conjugacy of Affine Actionson Compact Abelian GroupsMonatshefte für Mathematik, 129
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In this article, we study approximately topological conjugacies for continuous maps on compact metric spaces. It is proven that topological entropy generally is not an invariant for this equivalence. In particular, we discuss the approximately topologically conjugate classifications for circle homeomorphisms, rotations and automorphisms on torus. Mutually topological semi-conjugacy is also studied and compared with approximate topological conjugacy.
Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals
Published: May 1, 2022
Keywords: Approximate conjugacies; Semi-conjugacies; Circle homeomorphisms; Rotations; Automorphisms; Primary 54H20; Secondary 37E10; 37E45
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