Bifurcation in the Mathieu equation with three independent parameters
نویسندگان
چکیده
منابع مشابه
WKB and Resurgence in the Mathieu Equation
In this paper, based on lectures by the authors at the May 2015 workshop Resurgence, Physics and Numbers, at the Centro di Ricerca Matematica Ennio De Giorgio of the Scuola Normale Superiore in Pisa, we explain the origin of resurgent trans-series in the Mathieu equation spectral problem, using uniform WKB and all-orders (exact) WKB. Exact quantization conditions naturally arise, and their expa...
متن کاملCantor Spectrum for the Almost Mathieu Equation
Recently, there has been an explosion of interest in the study of Schrijdinger operators and Jacobi matrices with almost periodic potential (see, e.g., the review [ 161). The general belief is that generically the spectrum is a Cantor set, i.e., a nowhere dense perfect, closed set. Since it is easy to prove that the spectrum is closed and perfect (see, e.g., [2]), the key is to prove that the s...
متن کاملStability of the Damped Mathieu Equation With Time Delay
In the space of the system parameters, the stability charts are determined for the delayed and damped Mathieu equation defined as ẍ~t!1k ẋ~t!1~d1« cos t!x~t!5bx~t22p! . This stability chart makes the connection between the Strutt-Ince chart of the damped Mathieu equation and the Hsu-Bhatt-Vyshnegradskii chart of the autonomous second order delay-differential equation. The combined charts descri...
متن کاملt-expansion and the Mathieu Equation
The t-expansion, a nonperturbative analytic method for calculating the ground-state expectation values of arbitrary operators of the Hamiltonian, is applied to the Mathieu equation. Connrming previous results in other systems, a t-expansion up to order t 2 is suucient to recover the behaviour of the exact solution. A very good performance is observed when a variational wave function of the form...
متن کاملThe Asymptotics of the Gap in the Mathieu Equation
We provide a simple proof that the kth gap, A *, for the Mathieu operator-dz/dxs + 2~ cos (2x) is A& = 8(~/4)* [(k-l)!]-* (1 + o(k-s)), a result obtained (up to the value of an integral) by Harrell. The key observation is that what is involved is tunneling in momentum space.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 1980
ISSN: 0033-569X,1552-4485
DOI: 10.1090/qam/564734