A symplectic fixed point theorem on open manifolds

  title={A symplectic fixed point theorem on open manifolds},
  author={Michael R. Colvin and Kent E. Morrison},
In 1968 Bourgin proved that every measure-preserving, orientationpreserving homeomorphism of the open disk has a fixed point, and he asked whether such a result held in higher dimensions. Asimov, in 1976, constructed counterexamples in all higher dimensions. In this paper we answer a weakened form of Bourgin's question dealing with symplectic diffeomorphisms: every symplectic diffeomorphism of an even-dimensional cell sufficiently close to the identity in the C'-fine topology has a fixed point… 
3 Citations


D. G. Bourgin has proved that every measure-preserving orienta- tion-preserving homeomorphism of the open two-dimensional disk D has a fixed point. He suggested that the "result is perhaps valid even

Almost surely recurrent motions in the Euclidean space

We will show that measure-preserving transformations of Rn are recurrent if they satisfy a certain growth condition depending on the dimension n. Moreover, it is also shown that this condition is



A fixed point theorem in symplectic geometry

There are a number of fixed point theorems pecuhar to symplectic geometry. A particularly simple example is the theorem tha t any area-preserving mapping yJ of the two-dimensional sphere into itself

A bound for the fixed-point index of an area-preserving map with applications to mechanics

Carl P. Simon (Ann Arbor) Area-preserving maps and flows play an essential role in the study of motions of mechanical systems, especially in celestial mechanics (see [1, 14]). Since one is often

The obstruction to finding a boundary for an open manifold : of dimension greater than five

For dimensions greater than five the main theorem gives necessary and sufficient conditions that a smooth open manifold W be the interior of a smooth compact manifold with boundary. The basic

Mathematical Methods of Classical Mechanics

Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid


Find the secret to improve the quality of life by reading this foundations of mechanics, which can be your favorite book to read after having this book.

Periodic orbits of hamiltonian systems via critical point theory, manuscript

  • Lagrangian submanifolds and hamiltonian systems
  • 1971

Fixed points of diffeomorphisms on the two sphere that preserve area

  • Funkcional. Anal, i Prilozen
  • 1974