Bifurcations of topological type at singular points of parametrized vector fields

Shoshitaishvili, A. N.

doi:10.1007/bf01077527

Cited by 35 publications

(22 citation statements)

References 2 publications

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“…Since x(0)=[x&(0),xz (0) Pliss (1964) in the circumstance that there are no unstable modes (n"=0). Shoshitaishvili (1972Shoshitaishvili ( , 1975 The prefactor e '~e nforces h (x) -+0 as x~0 and h'(x)~0 as x -&0. Note that Eq.…”

Section: Period-doubling Bifurcationmentioning

confidence: 99%

Introduction to bifurcation theory

1991

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The theory of bifuxcation from equilibria based on center-manifold reduction and Poincare-Birkhoff normal forms is reviewed at an introductory level. Both differential equations and maps are discussed, and recent results explaining the symmetry of the normal form are derived. The emphasis is on the simplest generic bifurcations in one-parameter systems. Two applications are developed in detail: a Hopf bifurcation occurring in a model of thxee-wave xnode coupling and steady-state bifurcations occurring in the real Landau-Ginzburg equation. The forxner provides an example of the importance of degenerate bifurcations in problexns with more than one parameter and the latter illustxates new effects introduced into a bifurcation problexn by a continuous symmetry.

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Section: Period-doubling Bifurcationmentioning

confidence: 99%

Introduction to bifurcation theory

1991

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“…Our result is approximate , whereas Arnold (5) and Shoshaitshvili ( 6) show there exist transformations which eliminate the higher terms .…”

Section: )mentioning

confidence: 52%

Relaxation at critical points: Deterministic and stochastic theory

Mangel

1979

Physica A: Statistical Mechanics and its Applications

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“…Chapter 5 is devoted to establishing the non-autonomous counterpart to the HartmanGrobman Theorem for linearizing a mapping near a hyperbolic fixed point via a topological conjugacy and its generalization to the non-hyperbolic case due to Palmer [7] and Sositaisvili [14] where one obtains the product of a nonlinear flow on the centre manifold and a linear flow.…”

Section: Book Review 508mentioning

confidence: 99%

Geometric theory of discrete non-autonomous dynamical systems

Sacker

2013

Journal of Difference Equations and Applications

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Bifurcations of topological type at singular points of parametrized vector fields

Cited by 35 publications

References 2 publications

Introduction to bifurcation theory

Introduction to bifurcation theory

Relaxation at critical points: Deterministic and stochastic theory

Geometric theory of discrete non-autonomous dynamical systems

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