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Feb
6
awarded  Popular Question
Jan
24
awarded  Yearling
Nov
9
comment Linear ODE induces new ODE on the sphere: stability questions.
what is A in equation for $\dot{s}$?
Oct
30
comment Question about dense trajectory on $k$-dimensional torus under rotation map
"how to find angle of trajectory associated to rotation.": if the map takes ($x,y$) to $(x+\alpha_1,y+\alpha_2$), the angle is simply $tan^{-1}(\alpha_2/\alpha_1)$....
Oct
16
comment Linearization around a limit cycle versus stability of Poincare map
Floquet theory.
Sep
29
comment normal forms of vector fields reference
amazon.com/Introduction-Applied-Nonlinear-Dynamical-Mathematics/…
Sep
23
comment Find time-independent dynamical system equivalent to $x'=3x+(2-t)y$, $y'=xy-t$
just create another variable $z=t$, with $z'=1$. Replace all occurences of $t$ in your equations with $z$.
Sep
20
comment Complex Equilibrium Points in Dynamical Systems?
Because complex equilibrium points don't exist in $R^n$, they exist in $C^n$. For defining a dynamical system, you need to first define the phase space. Equilibrium points that don't exist in that phase space cannot be talked about.
Sep
18
comment Complex Equilibrium Points in Dynamical Systems?
If you define your dynamical systems to live in real space (say $R^n$), you cannot talk about complex equilibrium points. On the other hand, in the domain of complex dynamical systems, we do study complex equilibrium points.
Sep
2
comment References for methods for convergence analysis of discrete time dynamical systems with non lipschitz nonlinearity
Can you point out which technique for Lipschitz functions is failing for your case ?
Aug
30
answered Definition of topological entropy
Aug
25
revised Does Homoclinic tangle violate deterministic law?
added 467 characters in body
Aug
25
revised Does Homoclinic tangle violate deterministic law?
added 284 characters in body
Aug
25
answered Does Homoclinic tangle violate deterministic law?
Aug
23
answered Can someone explain the meaning of asymptotically stability in the following definition?
Aug
20
comment Computing $\bigtriangledown r^m$ knowing the vector $\boldsymbol r$
just use chain rule
Aug
18
reviewed No Action Needed Existence of solution to second order linear PDE
Aug
11
comment Any use of advanced Abstract Algebra in Differential Geometry?
Lie groups is an important part of differential geometry.
Aug
9
comment Relation between ergodic terms and probabilistic terms
stochastic process is not a deterministic dynamical system. See this:scholarpedia.org/article/Stochastic_dynamical_systems
Aug
9
comment Use Gronwall's lemma and method of successive approximations to show that a unique continuous solution exists on
Surely you mean to write the evolution of $x$ rather than $\mu$. $N_b(\mu_0)$ is the ball around parameter $\mu_0$ in $R^m$ in the same way $[-a,a]$ is the ball around $t=0$ in $R$.