Figure 1.
$f(s,t)=(s,s^3,t)$ is generalized transversal to $P=\{(0,0,z)\mid z\in \mathbb{R}\}$ mod $\mathbb{R}^3$
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October
2017, 10(5): 1043-1050.
doi: 10.3934/dcdss.2017055
A kind of generalized transversality theorem for $C^r$ mapping with parameter
| 1. | Department of Mathematics, Jilin University, Changchun, 130012, China |
| 2. | School of Science, Qiqihar University, Qiqihar, 161006, China |
The author considers a generalized transversality theorem of the mappings with parameter in infinite dimensional Banach space. If the mapping is generalized transversal to a single point set, and in the sense of exterior parameters, the mapping is a Fredholm operator, then there exists a residual set of parameter, such that the Fredholm operator is generalized transversal to the single point set.
Mathematics Subject Classification:
Primary: 46T05, 47A53; Secondary: 15A09.
Citation:
Qiang Li. A kind of generalized transversality theorem for $C^r$ mapping with parameter. Discrete and Continuous Dynamical Systems - S,
2017, 10
(5)
: 1043-1050.
doi: 10.3934/dcdss.2017055
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References:
| [1] |
K. C. Chang,
Methods in Nonlinear Analysis, Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2005. |
| [2] |
J. P. Ma,
(1-2) Inverses of operators between banach spaces and local conjugacy theorem, Chinese Ann. Math. Ser. B, 20 (1999), 57-62.
doi: 10.1142/S0252959999000084. |
| [3] |
J. P. Ma,
A generalized preimage theorem in global analysis, Sci. China. Ser. A, 44 (2001), 299-303.
doi: 10.1007/BF02878710. |
| [4] |
J. P. Ma,
A generalized transversality in global analysis, Pacific J.Math., 236 (2008), 357-371.
doi: 10.2140/pjm.2008.236.357. |
| [5] |
M. Z. Nashed,
Generalized Inverses and Applications, New York-San Francisco-London: Academic Pr. , 1976. |
| [6] |
E. Zeidler,
Nonlinear Functional Analysis and its Applications, Springer Verlag, New York-Berline, 1988.
doi: 10.1007/978-1-4612-4838-5. |
show all references
References:
| [1] |
K. C. Chang,
Methods in Nonlinear Analysis, Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2005. |
| [2] |
J. P. Ma,
(1-2) Inverses of operators between banach spaces and local conjugacy theorem, Chinese Ann. Math. Ser. B, 20 (1999), 57-62.
doi: 10.1142/S0252959999000084. |
| [3] |
J. P. Ma,
A generalized preimage theorem in global analysis, Sci. China. Ser. A, 44 (2001), 299-303.
doi: 10.1007/BF02878710. |
| [4] |
J. P. Ma,
A generalized transversality in global analysis, Pacific J.Math., 236 (2008), 357-371.
doi: 10.2140/pjm.2008.236.357. |
| [5] |
M. Z. Nashed,
Generalized Inverses and Applications, New York-San Francisco-London: Academic Pr. , 1976. |
| [6] |
E. Zeidler,
Nonlinear Functional Analysis and its Applications, Springer Verlag, New York-Berline, 1988.
doi: 10.1007/978-1-4612-4838-5. |
Figure 2.
$F(u,s)=(e^{u^2+s^2}-e,u^2+s^2-1)$ is generalized transversal to $P=\{\theta\}$ mod $\mathbb{R}^2$
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