Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas

Hans-Otto Walther

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1990

Abstract

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CONTENTSIntroduction...........................................................................................................................................5  I.........................................................................................................................................................151. Preliminaries...................................................................................................................................152. Solutions of a family of differential delay equations with periodic nonlinearity.................................163. Linearization of the semiflow............................................................................................................214. The saddle point property...............................................................................................................24  II........................................................................................................................................................305. The transformed semiflow...............................................................................................................306. A shift along the transformed semiflow............................................................................................367. The level sets H ⁺ a k ................................................................................................................448. Inclinations of tangent vectors.........................................................................................................469. Estimating D₁Σ(ψ,a) at BC-points ψ in level sets H ⁺ a k ............................................................4810. End of the proof of Theorem 6.1...................................................................................................51  III.......................................................................................................................................................5311. Šilnikov continuation and return map............................................................................................5312. Smoothness properties of f...........................................................................................................5613. Bifurcation.....................................................................................................................................5814. Proof of Theorem 13.2 (vi.2) and (vi.3), for a parameter interval A 19 instead of A...............6315. Proof of Theorem 13.2 (vi.1).........................................................................................................70References.........................................................................................................................................74

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Hans-Otto Walther. Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1990. <http://eudml.org/doc/268509>.

@book{Hans1990,
abstract = {CONTENTSIntroduction...........................................................................................................................................5  I.........................................................................................................................................................151. Preliminaries...................................................................................................................................152. Solutions of a family of differential delay equations with periodic nonlinearity.................................163. Linearization of the semiflow............................................................................................................214. The saddle point property...............................................................................................................24  II........................................................................................................................................................305. The transformed semiflow...............................................................................................................306. A shift along the transformed semiflow............................................................................................367. The level sets $H⁺_\{ak\}$................................................................................................................448. Inclinations of tangent vectors.........................................................................................................469. Estimating D₁Σ(ψ,a) at BC-points ψ in level sets $H⁺_\{ak\}$............................................................4810. End of the proof of Theorem 6.1...................................................................................................51  III.......................................................................................................................................................5311. Šilnikov continuation and return map............................................................................................5312. Smoothness properties of f...........................................................................................................5613. Bifurcation.....................................................................................................................................5814. Proof of Theorem 13.2 (vi.2) and (vi.3), for a parameter interval $A_\{19\}$ instead of A...............6315. Proof of Theorem 13.2 (vi.1).........................................................................................................70References.........................................................................................................................................74},
author = {Hans-Otto Walther},
keywords = {retarded functional differential equations; periodic nonlinearity; bifurcations of saddle connections; bifurcating periodic solutions; stable; attractive with asymptotic phase},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas},
url = {http://eudml.org/doc/268509},
year = {1990},
}

TY - BOOK
AU - Hans-Otto Walther
TI - Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas
PY - 1990
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction...........................................................................................................................................5  I.........................................................................................................................................................151. Preliminaries...................................................................................................................................152. Solutions of a family of differential delay equations with periodic nonlinearity.................................163. Linearization of the semiflow............................................................................................................214. The saddle point property...............................................................................................................24  II........................................................................................................................................................305. The transformed semiflow...............................................................................................................306. A shift along the transformed semiflow............................................................................................367. The level sets $H⁺_{ak}$................................................................................................................448. Inclinations of tangent vectors.........................................................................................................469. Estimating D₁Σ(ψ,a) at BC-points ψ in level sets $H⁺_{ak}$............................................................4810. End of the proof of Theorem 6.1...................................................................................................51  III.......................................................................................................................................................5311. Šilnikov continuation and return map............................................................................................5312. Smoothness properties of f...........................................................................................................5613. Bifurcation.....................................................................................................................................5814. Proof of Theorem 13.2 (vi.2) and (vi.3), for a parameter interval $A_{19}$ instead of A...............6315. Proof of Theorem 13.2 (vi.1).........................................................................................................70References.........................................................................................................................................74
LA - eng
KW - retarded functional differential equations; periodic nonlinearity; bifurcations of saddle connections; bifurcating periodic solutions; stable; attractive with asymptotic phase
UR - http://eudml.org/doc/268509
ER -

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