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Smoothness of Invariant Curves
2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Katznelson, Yitzhak, Ornstein, Donald S.
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Invariant Signatures of Closed Planar Curves
Journal of Mathematical Imaging and Vision, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
MUSSO, EMILIO, NICOLODI L.
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SIAM Journal on Mathematical Analysis, 1986
The main result concerns a smooth map T of a Banach space X into itself which has an unstable fixed point \(x_ 0\). We prove that if the spectral radius \(\lambda_ 0\) of the Fréchet derivative of T at \(x_ 0\) is an eigenvalue which exceeds one and appropriate additional assumptions hold, then there is a smooth invariant curve emanating from \(x_ 0 ...
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The main result concerns a smooth map T of a Banach space X into itself which has an unstable fixed point \(x_ 0\). We prove that if the spectral radius \(\lambda_ 0\) of the Fréchet derivative of T at \(x_ 0\) is an eigenvalue which exceeds one and appropriate additional assumptions hold, then there is a smooth invariant curve emanating from \(x_ 0 ...
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On Projective Invariants of Curves
Results in Mathematics, 1995The author computes invariants of plane curves for the isotropy group of a point in projective geometry (what one could call centro-projective geometry) depending on several \((< 4)\) points and derivatives. He also indicates possible invariant parameters for the corresponding configurations.
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Invariant rotational curves in Sitnikov's Problem
Celestial Mechanics & Dynamical Astronomy, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alfaro, J. Martínez, Chiralt, Cristina
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From Invariant Curves to Strange Attractors
Communications in Mathematical Physics, 2002A simple differential equation \(\ddot \theta +\lambda (\dot \theta-1) = \mu+\Phi (\theta)P_T(t)\) is studied as parameters are varied. Here, \(\Phi\) is \(2\pi\)-periodic, and \(P_T\) is \(T\)-periodic given by \(P_T(t)=1\) for \(t\in [0,t_0]\), while \(P_T(t)=0\) for \(t\in (t_0,T)\).
Wang, Qiudong, Young, Lai-Sang Young
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Computer Aided Geometric Design, 1986
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Pseudoautomorphisms with Invariant Curves
2015Inspired by constructions of automorphisms on rational surfaces and a recent paper of Perroni and Zhang (Mathematische Annalen 359(1–2):189–209, 2014), we give a concrete construction of pseudoautomorphisms of higher dimensional rational surfaces that have an invariant cuspidal curve and first dynamical degree larger than one.
Eric Bedford +2 more
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