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If $\omega_f(y) \subseteq \omega_f(x)$ and $int(\omega_f(y)) \neq \varnothing$ then $\omega_f(y) = \omega_f(x)$

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#metric-spaces #dynamical-systems #compactness #topological-dynamics
58
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Topological conjugacy of two dynamical systems

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#general-topology #matrices #ordinary-differential-equations #proof-writing #dynamical-systems
152
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Flow Box Theorem

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#general-topology #ordinary-differential-equations #dynamical-systems
42
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Integral curves for non-autonomous vector field that depends on a parameter

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#ordinary-differential-equations #dynamical-systems
72
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Computing the flow for a nonlinear ODE system

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#ordinary-differential-equations #dynamical-systems
65
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How do you show that orbits of $f(x)=x-x^3$ converge to $0$ for$-\sqrt{2} < x < \sqrt{2}$?

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#real-analysis #calculus #dynamical-systems
74
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Construction of the topological equivalence homeomorphism

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#ordinary-differential-equations #dynamical-systems
47
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Meaning of complex eigenvalues for 2D matrix realtive to dynamical systems

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#eigenvalues-eigenvectors #dynamical-systems #stability-theory #linearization
97
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Show that $\dot x = x + u, y = x$ is time-invariant.

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#ordinary-differential-equations #proof-writing #dynamical-systems #control-theory #signal-processing
41
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From local flows to global flows of ODEs

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#ordinary-differential-equations #dynamical-systems
96
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Smoothness of the local flow. Intuition behind the proof

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#real-analysis #ordinary-differential-equations #dynamical-systems
47
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Multiplying sequence of $3\times 3$ matrices

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#linear-algebra #matrices #stochastic-processes #dynamical-systems
37
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Inferring information about the Jacobian matrix at the fixed point based on the configuration of the nullclines

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#ordinary-differential-equations #dynamical-systems
63
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(Explaination of) Proof of Global Stable Manifold Theorem in Audin & Damian's book

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#proof-explanation #dynamical-systems #morse-theory #gradient-flows
59
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Question from Katok and Hasselblat (page 724, proof of the Poincare Lemma)

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#differential-geometry #dynamical-systems #differential-forms

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