All Questions
Tagged with ds.dynamical-systems mp.mathematical-physics
12 questions
164
votes
14
answers
40k
views
What is an integrable system?
What is an integrable system, and what is the significance of such systems? (Maybe it is easier to explain what a non-integrable system is.) In particular, is there a dichotomy between "...
- 24.7k
18
votes
2
answers
2k
views
Renormalization in physics vs. dynamical systems
I am studying complex dynamics, so to me renormalization of a dynamical system means something like a rescaled first-return map on (a subset of) the underlying space. I understand that in quantum ...
- 181
23
votes
1
answer
4k
views
The Dedekind eta function in physics
This interesting little fellow (a nice introduction is the video "Mock Modular Forms are Everywhere" by Cheng and Felder) popped up in some operator algebra (Witt / Virasoro Lie algebra) I ...
6
votes
2
answers
3k
views
What's the probability distribution of a deterministic signal or how to marginalize dynamical systems? (functional integrals in probability theory)
Because I still have no idea how it is possible for me to write down seemingly important equations ... that don't make any sense (at least for me) and because I haven't got any helpful comment so far, ...
- 1,026
4
votes
0
answers
327
views
The Moyal action of a planar vector field
Let $X=P\frac{\partial}{\partial x}+Q\frac{\partial}{\partial y}$ be a polynomial vector field on $\mathbb{R}^{2}$. Consider the following (Moyal) operator on $\mathbb{C}[x,y]$:
$\tilde{D}_{X}(f)=...
- 356
27
votes
4
answers
13k
views
Hamiltonian, Lagrangian and Newton formalism of mechanics
If my thinking is wrong please let me know. I have little knowledge on beyond-college physics.
For research purposes, I read a few introductions to these three formalisms of classical mechanics [1,2,...
- 8,071
16
votes
2
answers
2k
views
Why is every symplectomorphism of the unit disk Hamiltonian isotopic to the identity?
That is, for any symplectomorphism $\psi: D^2 \to D^2$, there should be a time-dependent Hamiltonian Ht on D2 such that the corresponding flow at time 1 is equal to $\psi$.
I found this in claim a ...
- 3,203
13
votes
2
answers
2k
views
Simple example of renormalization
As far as I understand, the RG theory, or functional RG theory is a mathematical tool for moving in the "scale dimension". The tool can be used for calculation of Feigenbaums constant (e.g. mentioned ...
- 175
12
votes
1
answer
735
views
Parametrisations for null temperature functions: nonuniqueness of solutions to the heat equation
Disclaimer. I expect this is a highly open problem, but maybe I'm wrong and someone has come up with some answers besides those given here. In any case, all information appreciated, thanks!
Definition....
- 1,990
9
votes
1
answer
726
views
When does a Lagrangian dynamical system have an equivalent Hamiltonian description?
Let a Lagrangian dynamical system with $n$ degrees of freedom and configuration space $\mathbb{R}^n$
(i.e. phase space $\mathbb{R}^{2n}$), which is described by $L=L(q_{i},\dot{q}_{i},t)$, $i=1,2,......
- 7,746
8
votes
3
answers
5k
views
Bertrand theorem - central forces
Here is a version of Bertrand theorem. Let us consider a force $F(r)$ which depends only on the distance to a given point. If all trajectories which remain bounded are closed, then either $F(r)=ar$ ...
- 551
2
votes
0
answers
491
views
Is there a Bayesian theory of deterministic signal? Prequel and motivation for my previous question
This is a prequel to my question:
What's the probability distribution of a deterministic signal or how to marginalize dynamical systems? (functional integrals in probability theory)
Clearly my ...
- 1,026