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A Polynomial Counterexample to the Markus–Yamabe Conjecture
A Polynomial Counterexample to the Markus–Yamabe Conjecture,10.1006/aima.1997.1673,Advances in Mathematics,Anna Cima,Arno van den Essen,Armengol Gasul
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A Polynomial Counterexample to the Markus–Yamabe Conjecture
(
Citations: 27
)
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Anna Cima
,
Arno van den Essen
,
Armengol Gasull
,
Engelbert Hubbers
,
Francesc Mañosas
We give a polynomial counterexample to both the Markus–Yamabe conjecture and the discrete Markus–Yamabe problem for all dimensions ⩾3.
Journal:
Advances in Mathematics  ADVAN MATH
, vol. 131, no. 2, pp. 453457, 1997
DOI:
10.1006/aima.1997.1673
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Citation Context
(13)
...
9
give an example of a polynomial vector field having orbits that escape to infinity which satisfies the MYC hypotheses...
Víctor Guíñez
,
et al.
A polynomial class of Markus–Yamabe counterexamples and examples in ℝ
...Unlike in the 2D case it does not follow that the equilibrium is globally stable, since the MarkusYamabe conjecture does not hold in dimensions greater than 2 [
21
]...
...Since the MarkusYamabe conjecture does not hold in dimensions greater than 2 [
21
], global stability does not follow automatically from local stability, and requires independ ent proof...
Pete Donnell
,
et al.
Stability in generic mitochondrial models
...to the Jacobian conjecture, see [
4
, 7, 8]. One of the conjectures which was posed and killed “along the way” of this story was Meister’s Linearization conjecture (see page 186 of [6] or [5])...
Stefan Maubach
,
et al.
The Nagata automorphism is shifted linearizable
...gif"/> [
6
]...
M. Furi
,
et al.
Global stability of equilibria
...After all, similar statements, like the Jacobian Conjecture for reals (see [12]) and the Jacobian Conjecture for dynamical systems (the MarkusYamabe conjecture, see[
3
]) are not true...
Stefan Maubach
,
et al.
Maps that are roots of power series
References
(4)
Global asymptotic stability of differential equations in the plane
(
Citations: 13
)
A GASULL
,
J LLIBRE
,
J SOTOMAYOR
Journal:
Journal of Differential Equations  J DIFFERENTIAL EQUATIONS
, vol. 91, no. 2, pp. 327335, 1991
Global stability criteria for differential systems
(
Citations: 23
)
Lawrence Markus
,
Hidehiko Yamabe
Published in 1960.
Jacobian problems in differential equations and algebraic geometry
(
Citations: 13
)
Gary H. Meisters
Journal:
Rocky Mountain Journal of Mathematics  ROCKY MT J MATH
, vol. 12, no. 1982, pp. 679706, 1982
Solution of the Global Asymptotic Stability Jacobian Conjecture for the Polynomial Case
(
Citations: 13
)
G. H. Meisters
,
Cz. Olech
Published in 1988.
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Citations
(27)
A polynomial class of Markus–Yamabe counterexamples and examples in ℝ
Víctor Guíñez
,
Álvaro Castañeda
Journal:
Applicable Analysis
, vol. 90, no. 5, pp. 787798, 2011
Nuclear physics experiments for the astrophysical p process
A. Sauerwein
,
M. Elvers
,
J. Endres
,
J. Hasper
,
A. Hennig
,
L. Netterdon
,
A. Zilges
Journal:
Progress in Particle and Nuclear Physics  PROG PART NUCL PHYS
, vol. 66, no. 2, pp. 363367, 2011
Stability in generic mitochondrial models
(
Citations: 4
)
Pete Donnell
,
Murad Banaji
,
Stephen Baigent
Journal:
Journal of Mathematical Chemistry  J MATH CHEM
, vol. 46, no. 2, pp. 322339, 2009
The Nagata automorphism is shifted linearizable
(
Citations: 1
)
Stefan Maubach
,
PierreMarie Poloni
Journal:
Journal of Algebra  J ALGEBRA
, vol. 321, no. 3, pp. 879889, 2009
A note on the divergencefree Jacobian Conjecture in R^2
(
Citations: 1
)
Marco Sabatini
Journal:
Bulletin of The Polish Academy of Sciences Mathematics
, vol. 57, no. 2, pp. 109115, 2009