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Periods of Morse-Smale diffeomorphisms of 𝕊²

100%

Guirao J., Llibre J.

Colloquium Mathematicum

2008

tom 110

nr 2

477-483

The aim of this paper is to describe the set of periods of a Morse-Smale diffeomorphism of the two-dimensional sphere according to its homotopy class. The main tool for proving this is the Lefschetz fixed point theory.

Dynamics of a Lotka-Volterra map

81%

Balibrea F., Guirao J., Lampart M., Llibre J.

Fundamenta Mathematicae

2006

tom 191

nr 3

265-279

Given the plane triangle with vertices (0,0), (0,4) and (4,0) and the transformation F: (x,y) ↦ (x(4-x-y),xy) introduced by A. N. Sharkovskiĭ, we prove the existence of the following objects: a unique invariant curve of spiral type, a periodic trajectory of period 4 (given explicitly) and a periodic trajectory of period 5 (described approximately). Also, we give a decomposition of the triangle which helps to understand the global dynamics of this discrete system which is linked with the behavior of the Schrödinger equation.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Fundamenta Mathematicae

2 Guirao J.

2 Llibre J.

1 Balibrea F.

1 Lampart M.

1 2008

1 2006

Wyniki wyszukiwania

Periods of Morse-Smale diffeomorphisms of 𝕊²

Dynamics of a Lotka-Volterra map