The board of the trust has written to shareholders saying it will "review carefully" proposed arrangements for the management of the company.
The trust, which still has strong support from Scottish investors, is chaired by Scots accountant Jim Pettigrew, former chief at CMC Markets and also a non-executive at Aberdeen Asset Management, and has three senior Scottish financial figures on its board - former investment chiefs Dick Barfield (Standard Life) and Max Ward (Baillie Gifford) and former Bank of Scotland executive Gordon McQueen.
Shares slumped by 5% on October 15 when Mr Woodford's departure was announced, and were down 3p at 569p yesterday.
The trust has underperformed its sector over the past year, ranking 20th out of 25 UK growth and income trusts, according to Investment Life & Pensions Moneyfacts. Over three years, it ranks seventh and over five years fifth, turning £1000 into £2259, compared with £1387 for the all-share index and £1911 for the sector. However, the trust is ranked fourth out of 18 trusts over 10 years, which includes six years under previous manager Fidelity, which won the then £1.4bn trust from Edinburgh Fund Managers in 2002 and ran it until 2009.
Simon Elliott, investment trust analyst at Winterflood Securities, said: "Invesco will be keen to retain the management contract for the fund, which has assets of £1.35bn and has performed well since its move. However, the fund's board is certainly independent, as evidenced by its willingness to move the management of the investment trust twice in the last 11 years."
Mr Elliott said Mr Woodford, who manages £11bn in total for Invesco, had "developed a formidable track record from unconstrained long-term investing".
"It comes as no surprise that Mark Barnett has been appointed as Woodford's successor," he said. "They have worked together for 17 years and the two managers broadly share the same investment approach and views. If anything, Mark has enjoyed the stronger performance record of late, benefiting from his mid-cap bias and less defensive stance."