A New Proof of Moser's Theorem

Liu, Chang; Xing, Jiamin

doi:10.11948/20220161

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The Intersection Property In Dimension Two1

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2022

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“…We do not consider here multidimensional generalizations of the intersection property. Recent works on this subject are exemplified by the papers [22,37].…”

Section: The Intersection Property In Dimension Twomentioning

confidence: 99%

Three Examples in the Dynamical Systems Theory

Sevryuk¹

2022

SIGMA

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We present three explicit curious simple examples in the theory of dynamical systems. The first one is an example of two analytic diffeomorphisms R, S of a closed twodimensional annulus that possess the intersection property but their composition RS does not (R being just the rotation by π/2). The second example is that of a non-Lagrangian n-torus L 0 in the cotangent bundle T * T n of T n (n ≥ 2) such that L 0 intersects neither its images under almost all the rotations of T * T n nor the zero section of T * T n . The third example is that of two one-parameter families of analytic reversible autonomous ordinary differential equations of the form ẋ = f (x, y), ẏ = µg(x, y) in the closed upper half-plane {y ≥ 0} such that for each family, the corresponding phase portraits for 0 < µ < 1 and for µ > 1 are topologically non-equivalent. The first two examples are expounded within the general context of symplectic topology.

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“…We do not consider here multidimensional generalizations of the intersection property. Recent works on this subject are exemplified by the papers [22,37].…”

Section: The Intersection Property In Dimension Twomentioning

confidence: 99%

Three Examples in the Dynamical Systems Theory

Sevryuk¹

2022

SIGMA

View full text Add to dashboard Cite

show abstract

A New Proof of Moser's Theorem

Cited by 1 publication

References 15 publications

Three Examples in the Dynamical Systems Theory

Three Examples in the Dynamical Systems Theory

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