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Results tagged with ds.dynamical-systems
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user 30684
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
0
votes
Lyapunov exponents for PDEs
I am aware of a few "applied" papers where this is done:
http://pre.aps.org/abstract/PRE/v75/i4/e045203
http://pre.aps.org/abstract/PRE/v85/i4/e046201
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4
votes
What are the Poincaré invariants for a specific interesting low-dimensional (4 or 6) Hamilto...
Please see: Maruskin, Jared M., Daniel J. Scheeres, and Anthony M. Bloch. "Dynamics of symplectic subvolumes." SIAM Journal on Applied Dynamical Systems 8.1 (2009): 180-201.
Scheeres, D. J., et al. " …
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1
vote
What are good references for spatial dynamics?
Robinson: Infinite-Dimensional Dynamical Systems: An Introduction
to Dissipative Parabolic PDEs and the Theory of Global Attractors
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1
vote
Making a system of second-order ODEs chaotic
You can get chaos with a cubic term for $x_1$.
In applied dyanmical systems, there has been considerable interest in last decade to study systems of the following form:
$\ddot{x_1}=-ax_1^3+\epsilon(x_ …
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3
votes
Accepted
examples of surface diffeomorphism that exhibit heteroclinic bifurcation?
It cannot happen in a continuous time 2D system, simply due to uniqueness of ODE property. At least (2+1)-D is needed, i.e. this phenomenon can be seen in 2D maps derived from taking time-T sections o …
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3
votes
Knots and Dynamics. Recent breakthroughs?
IF you are willing to extend into "braid theory and dynamics", there is quite a bit of activity in the field of "topological fluid mechanics" in last decade.
Some of this work is directed at determi …
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1
vote
Applications of discrete-time dynamics
Many systems are best probed stroboscopically. For e.g. in the design of space mission trajectories, it is customary to use the restricted-three body problem as the model for dynamics of the spacecraf …
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4
votes
Accepted
Proving period doubling bifurcation
It would be quite hard to give a purely analytical proof for continuous systems, since period doubling analysis (which is typically via Lyapunov-Schmidt bifurcation theory) will need to be carried on …
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4
votes
Restricted Three-Body Problem
The problem of 'optimal path' for going to moon has been studied under the topic of "Circular Restricted three-body problem" and "Planar circular three-body problem (PCR3BP)". Poincare' made major con …
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4
votes
1
answer
251
views
Boundary flux maximizing drift (velocity) vector fields for 2D heat equation
Looking for literature / known results on the following class of problems:
Consider the domain bounded, open $\Omega\in \mathbb R^2$ with smooth boundary, divergence free drift $u=u(x,t)$, scalar fie …
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15
votes
Accepted
Steepest descent/gradient descent as dynamical system
This topic has long history. Here are some references:
Bloch, Anthony M. "Steepest descent, linear programming and Hamiltonian flows." Contemp. Math. AMS 114 (1990): 77-88.
Brockett, Roger W. Dynami …
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1
vote
Measuring how suboptimal control is
Model predictive control (MPC, aka receding horizon control) is one type of sub-optimal control method that is extremely well studied and popular. The "sub-optimality" of this type of control methods …
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1
vote
Good books on Geometric Theory of Dynamical Systems
I guess "Geometrical Methods in the Theory of Ordinary Differential Equations" by Arnold should be in the list too, although it doesn't satisfy the "purely" topological criteria.
2
votes
Accepted
Reference request: Invariant sets of dynamical systems
I am assuming you are interested in multidimensional case $x\in\mathbb R^n$.
Let $\Omega$ be the set whose invariance you are interested in estabilishing.
There are two types of problems here:
A). …
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9
votes
Book on the Three body Problem
For the Restricted three-body problem, I suggest:
Dynamical Systems, the Three-Body Problem and Space Mission Design By Marsden,Koon,Lo and Ross Available free at: www2.esm.vt.edu/~sdross/books
This …
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