An eigenvalue condition and the equivalence of two-dimensional maps

Roland Rabanal

doi:10.1080/10236198.2022.2055471

An eigenvalue condition and the equivalence of two-dimensional maps

Roland Rabanal

Sección de Matemáticas

Research output: Contribution to journal › Article › peer-review

Abstract

The condition on (Formula presented.) -maps of (Formula presented.) into itself is the assumption that their Jacobian eigenvalues are all equal to one (unipotent maps). A unipotent (Formula presented.) -map (Formula presented.) is equivalent to the translation (Formula presented.) if the map is fixed-point-free. It provides a one parameter family of (Formula presented.) -maps (Formula presented.) such that (Formula presented.) is linearly conjugated to G, (Formula presented.) has a global attractor for (Formula presented.) and a global repeller for (Formula presented.).

Original language	English
Pages (from-to)	578-589
Number of pages	12
Journal	Journal of Difference Equations and Applications
Volume	28
Issue number	4
DOIs	https://doi.org/10.1080/10236198.2022.2055471
State	Published - 2022

Keywords

14R15
26B10
37C15
37E30
Discrete Markus–Yamabe problem
global dynamics
Jacobian conjecture
Unipotent maps

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10.1080/10236198.2022.2055471

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title = "An eigenvalue condition and the equivalence of two-dimensional maps",

abstract = "The condition on (Formula presented.) -maps of (Formula presented.) into itself is the assumption that their Jacobian eigenvalues are all equal to one (unipotent maps). A unipotent (Formula presented.) -map (Formula presented.) is equivalent to the translation (Formula presented.) if the map is fixed-point-free. It provides a one parameter family of (Formula presented.) -maps (Formula presented.) such that (Formula presented.) is linearly conjugated to G, (Formula presented.) has a global attractor for (Formula presented.) and a global repeller for (Formula presented.).",

keywords = "14R15, 26B10, 37C15, 37E30, Discrete Markus–Yamabe problem, global dynamics, Jacobian conjecture, Unipotent maps",

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AB - The condition on (Formula presented.) -maps of (Formula presented.) into itself is the assumption that their Jacobian eigenvalues are all equal to one (unipotent maps). A unipotent (Formula presented.) -map (Formula presented.) is equivalent to the translation (Formula presented.) if the map is fixed-point-free. It provides a one parameter family of (Formula presented.) -maps (Formula presented.) such that (Formula presented.) is linearly conjugated to G, (Formula presented.) has a global attractor for (Formula presented.) and a global repeller for (Formula presented.).

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KW - 37C15

KW - 37E30

KW - Discrete Markus–Yamabe problem

KW - global dynamics

KW - Jacobian conjecture

KW - Unipotent maps

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An eigenvalue condition and the equivalence of two-dimensional maps

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Keywords

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