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https://doi.org/10.12775/TMNA.2021.004Słowa kluczowe
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E.C. Balreira, Incompressibility and global inversion, Topol. Methods Nonlinear Anal. 35 (2010), 69–76.
H. Bass, E. Connell and D. Wright, The Jacobian Conjecture: reduction of degree and formal expansion of the inverse, Bull. Amer. Math. Soc. 7 (1982), 287–330.
F. Braun, L.R.G. Dias and J. Venato-Santos, On topological approaches to the Jacobian conjecture in Cn , Proc. Edinb. Math. Soc. 63 (2020), 666–675.
M. Cobo, C. Gutierrez and J. Llibre, On the injectivity of C 1 maps of the real plane, Canad. J. Math. 54 (2002), 1187–1201.
M. Coste and M.J. de la Puente, Atypical values at infinity of a polynomial function on the real plane: an erratum, and an algorithmic criterion, J. Pure Appl. Algebra 162 (2001), 23–35.
S. Cynk and K. Rusek, Injective endomorphisms of algebraic and analytic sets, Ann. Polon. Math. 56 (1991), 29–35.
G. de Marco, Fibrations of real valued functions, Nonlinear Anal. 28 (1997), 1689–1695.
L.R.G. Dias, M.A.S. Ruas and M. Tibăr, Regularity at infinity of real mappings and a Morse–Sard theorem, J. Topol. 5 (2012), 323–340.
A. Fernandes, C. Gutierrez and R. Rabanal, Global asymptotic stability for differentiable vector fields of R2 , J. Differential Equations 206 (2004), 470–482.
A. Fernandes, C. Maquera and J. Venato-Santos, Jacobian conjecture and semialgebraic maps, Math. Proc. Cambridge Philos. Soc. 157 (2014), 221–229.
T. Gaffney, Fibers of polynomial mappings at infinity and a generalized Malgrange condition, Compos. Math. 119 (1999), 157–167.
C. Gutierrez, A solution to the bidimensional global asymptotic stability conjecture, Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995), 627–671.
C. Gutierrez, X. Jarque, J. Llibre and M.A. Teixeira, Global injectivity of C 1 maps of the real plane, inseparable leaves and the Palais-Smale condition, Canad. Math. Bull. 50 (2007), 377–389.
C. Gutierrez and C. Maquera, Foliations and polynomial diffeomorphisms of R3 , Math. Z. 262 (2009), 613–626.
Z. Jelonek, The set of points at which a polynomial map is not proper, Ann. Polon. Math. 58 (1993), 259–266.
Z. Jelonek, Testing sets for properness of polynomial mappings, Math. Ann. 315 (1999), 1–35.
Z. Jelonek, Geometry of real polynomial mappings, Math. Z. 239 (2002), 321–333.
Z. Jelonek, On asymptotic critical values and the Rabier theorem, Geometric Singularity Theory, vol. 65, Banach Center Publ., Polish Acad. Sci. Inst. Math., Warsaw, 2004, pp. 125–133.
C. Joiţa and M. Tibăr, Bifurcation set of multi-parameter families of complex curves, J. Topol. 11 (2018), 739–751.
C. Joiţa and M. Tibăr, Bifurcation values of families of real curves, Proc. Roy. Soc. Edinburgh Sect. A 147 (2017), 1233–1242.
O.-H. Keller, Ganze Cremona-transformationen, Monatsh. Math. Phys. 47 (1939), 299–306.
T. Krasiński and S. Spodzieja, On linear differential operators related to the ndimensional Jacobian conjecture, Real Algebraic Geometry, Lect. Notes Math., vol. 1524, Springer–Verlag, 1992, pp. 308–315.
K. Kurdyka, P. Orro and S. Simon, Semialgebraic Sard theorem for generalized critical values, J. Differential Geom. 56 (2000), 67–92.
C. Maquera and J. Venato-Santos, Foliations and global injectivity in Rn , Bull. Braz. Math. Soc. 44 (2013), 273–284.
S. Nollet and F. Xavier, Global inversion via the Palais–Smale condition, Discrete Contin. Dyn. Syst. 8 (2002), 17–28.
T. Parthasarathy, On Global Univalence Theorems, Lect. Notes Math., vol. 977. Springer–Verlag, Berlin, New York, 1983, viii+106 pp.
A. Parusiński, On the bifurcation set of complex polynomial with isolated singularities at infinity, Compos. Math. 97 (1995), 369–384.
L. Păunescu and A. Zaharia, On the Lojasiewicz exponent at infinity for polynomial functions, Kodai Math. J. 20 (1997), 269–274.
S. Pinchuck, A counterexample to the strong real Jacobian conjecture, Math. Z. 217 (1994), 1–4.
P.J. Rabier, Ehresmann fibrations and Palais–Smale conditions for morphisms of Finsler manifolds, Ann. of Math. 146 (1997), 647–691.
M. Sabatini, An extension to Hadamard global inverse function theorem in the plane, Nonlinear Anal. 20 (1993), 1069–1077.
D. Siersma and M. Tibăr, Singularities at infinity and their vanishing cycles, Duke Math. J. 80 (1995), 771–783.
N. Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N.J., 1951, viii+224 pp.
M. Tibăr and A. Zaharia, Asymptotic behaviour of families of real curves, Manuscripta Math. 99 (1999), 383–393.
L.D. Tráng and C. Weber, A geometrical approach to the Jacobian conjecture for n = 2, Kodai Math. J. 17 (1994), 374–381.
A. van den Essen, Polynomial automorphisms and the Jacobian conjecture, Progress in Mathematics, 190. Birkhäuser Verlag, Basel, 2000, xviii+329 pp.
H.H. Vui and L.D. Tráng, Sur la topologie des polynômes complexes, Acta Math. Vietnam. 9 (1984), 21–32.
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