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How to show that every non-trivial orbit of ODE is periodic

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#ordinary-differential-equations #dynamical-systems #periodic-functions
253
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Consider the system $x'=-y-x^2$, $y'=x.$ Find a reversor $S$, identify Fix$(S)$ and show that the origin is a nonlinear center.

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#ordinary-differential-equations #systems-of-equations #dynamical-systems #nonlinear-system #linearization
43
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Does stability along axes imply stability of the fixed point?

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#dynamical-systems #stability-theory #fixed-points #nonlinear-dynamics
63
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How to linearise $\dot \epsilon_y = (a+\epsilon_y)(1- \frac{a+\epsilon_y}{a+\epsilon_x})$?

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#dynamical-systems #nonlinear-system #stability-in-odes #perturbation-theory #fixed-points
140
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The stability of a fixed point, given that the one of the eigenvalues of the linearised system is zero and the other it negative?

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#dynamical-systems #nonlinear-system #perturbation-theory #stability-theory #nonlinear-dynamics
575
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Is there an analytic way to tell if a system of ordinary differential equations is conservative?

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#ordinary-differential-equations #dynamical-systems #jacobian
63
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Distance of perturbed flow from the unperturbed stable manifold

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#dynamical-systems #perturbation-theory #nonlinear-dynamics
18
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Extending the solution of an ODE to arbitrarily large times in dimension $\geqslant 5$

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#ordinary-differential-equations #dynamical-systems
23
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Equivalent definitions of $C^*$-systems.

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#operator-theory #dynamical-systems #operator-algebras #automorphism-group
25
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What is the unstable space of $0$ with respect to this matrix

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#linear-algebra #dynamical-systems
69
Views

Problem understanding passage from explicit representation to implicit representation

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#ordinary-differential-equations #dynamical-systems #control-theory #linear-control
38
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fixed points of a system of ODEs

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#ordinary-differential-equations #dynamical-systems #fixed-points
179
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Explicit solutions of equations similar to predator-prey

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#ordinary-differential-equations #dynamical-systems #nonlinear-system
69
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Markov chains are positive/completely positive...?

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#operator-theory #dynamical-systems #markov-chains #markov-process
72
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The stable and unstable sets of the torus are dense

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#real-analysis #calculus #abstract-algebra #dynamical-systems

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