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Results tagged with ds.dynamical-systems
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user 12482
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
9
votes
A vector field on the tangent bundle which is not equivalent to any second order ODE
I guess you want the topological equivalence to preserve the bundle structure of $TM \longrightarrow M$ otherwise it becomes a bit arbitrary, right?
In this case a non-zero vertical vector field will …
- 8,098
6
votes
0
answers
201
views
The geometric shape of domains of flows
Consider a smooth (non-compact) manifold $M$ with a vector field $X$. Then we know that there is a open neighbourhood $U \subseteq M \times \mathbb{R}$ of $M \times \{0\}$ such that on $U$ the flow $\ …
- 8,098
5
votes
Geometry and Integrability in Other Bundles
As it was already pointed out, on a bare vector bundle there is no intrinsic notion of "integrability". However, things change when you pass to a Lie algebroid: In this case the vector bundle $E$ is e …
- 8,098
0
votes
Good books on Geometric Theory of Dynamical Systems
Mainly from the Hamiltonian point of view:
Zehnder: Lectures on Dynamical Systems