The discrete Markus–Yamabe problem

DOI10.1016/S0362-546X(97)00715-3zbMath0919.34042OpenAlexW2003660726MaRDI QIDQ4238341

Anna Cima, Armengol Gasull, Francesc Mañosas

Publication date: 25 August 1999

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(97)00715-3

zbMATH Keywords

global attractorsdiscrete time systemsMarkus-Yamabe conjecturetriangular maps

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Attractors of solutions to ordinary differential equations (34D45) Differentiable maps on manifolds (58C25) Dynamical systems and ergodic theory (37-XX)

Related Items (27)

Nilpotent symmetric Jacobian matrices and the Jacobian conjecture ⋮ Global injectivity of differentiable maps via \(W\)-condition in \(\mathbb{R}^2\) ⋮ Markus-Yamabe conjecture for non-autonomous dynamical systems ⋮ An eigenvalue condition and the equivalence of two-dimensional maps ⋮ Some results about global asymptotic stability ⋮ Horseshoes for a generalized Markus-Yamabe example ⋮ Remarks on the Belitskii-Lyubich and discrete Markus-Yamabe conjectures ⋮ Markus-Yamabe's conjecture for compact gradients in Hilbert spaces ⋮ The discrete Markus-Yamabe problem for symmetric planar polynomial maps ⋮ Planar embeddings with a globally attracting fixed point ⋮ Asynchronous Boolean networks and hereditarily bijective maps ⋮ On differentiable area-preserving maps of the plane ⋮ Local cycles and dynamical properties of Boolean networks ⋮ Global asymptotic stability for differentiable vector fields of \(\mathbb R^2\) ⋮ A reduction of the Jacobian Conjecture to the symmetric case ⋮ Note on the Markus--Yamabe conjecture for gradient dynamical systems ⋮ Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem ⋮ A single particle impact model for motion in avalanches ⋮ Planar maps whose second iterate has a unique fixed point ⋮ Asymptotically stable heteroclinic cycles in discrete-time -equivariant cubic dynamical systems ⋮ Global stability of equilibria ⋮ Dynamics of maps with nilpotent Jacobians ⋮ Some open problems in low dimensional dynamical systems ⋮ A counterexample to Meisters' cubic-linear linearization conjecture ⋮ Global stability of a class of difference equations on solvable Lie algebras ⋮ The Jacobian conjecture: Linear triangularization for homogeneous polynomial maps in dimension three ⋮ Nilpotent Jacobians in dimension three

Cites Work

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• Chaotic polynomial automorphisms: Counterexamples to several conjectures
• On the Kalman problem
• Polynomials with constant Hessian determinant
• A new class of invertible polynomial maps
• A polynomial counterexample to the Markus-Yamabe conjecture
• Polynomial automorphisms and the Jacobian conjecture
• A solution to the bidimensional global asymptotic stability conjecture
• Über die Lösungen der Differentialgleichung \({r t - s^2 = 1}\)
• The Jacobian conjecture: Reduction of degree and formal expansion of the inverse
• Chebyshev-Haar systems in the theory of discontinuous Kellogg kernels
• A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization

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