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The only definition I have so far is that the suspension flow denoted by $\sigma ^t_f$ is determined by the "vertical" vector field $\frac{\partial}{\partial t}$ on $M_f$ (the suspension manifold), then to get use to this $\sigma ^t_f$ I picked up the easiest $M$, an interval, so I'm asking the following:

Let $M=[0,1]$ and $f(x)=1-x$ then I now that the suspension manifold with respect to $f$, $M_f$, is homeomorphic to the Mobius strip, since $M_f$ is only a rotation and translation of it, then, since I don't know it looks like, I would like to know characteristics about the suspension flow, like

1) how many orbits with period one or two does it have?,

2) if it has period one/two orbits, does they separate $M_f$?,

3) and if someone does, then How many and how are those pieces?

Thanks in advance for your help.

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    Do you know about Poincare sections? Or about correspondence between periodic points of mapping $f$ on $M$ and periodic orbits of $\sigma^t_f$ on $M_f$ ? – 2017-02-28
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    No, Can you elaborate please :) Thanks for your comment – 2017-02-28
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    So what can you tell me :) @Evgeny – 2017-02-28
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    It would be nice to know what other methods have you covered in this course. – 2017-02-28
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    Well the thing is that I am only a beginner in this setting of dynamical systems, then I have only seen the notions, like an intuitive definition and what is going to be the main purpose of studying this so no methods have been covered yet :) – 2017-02-28
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    Then what do you think @Evgeny :) – 2017-02-28
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    Sorry, but I don't have time for a full answer right now. I can suggest you the following experiment: if you understand how suspension flow works, try to describe the behaviour of trajectory starting at $(1/3, 0) \in M_f$. – 2017-02-28
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    @Evgeny Ok, but that is the problem, I don't have any explicit suspension flow to work with, and even an explicit definition either :) I can wait for you explicit answer, no problem, if you agree of course :) – 2017-02-28
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    Then @Evgeny How can one proceed? Thanks :) – 2017-03-06

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